diff --git a/poincare/include/poincare/absolute_value.h b/poincare/include/poincare/absolute_value.h
index 2aad1feed..357198c54 100644
--- a/poincare/include/poincare/absolute_value.h
+++ b/poincare/include/poincare/absolute_value.h
@@ -55,7 +55,7 @@ public:
   static Expression UntypedBuilder(Expression children) { return Builder(children.childAtIndex(0)); }
   static constexpr Expression::FunctionHelper s_functionHelper = Expression::FunctionHelper("abs", 1, &UntypedBuilder);
 
-  Expression shallowReduce(Context & context, Preferences::AngleUnit angleUnit);
+  Expression shallowReduce(Context & context, Preferences::AngleUnit angleUnit, ExpressionNode::ReductionTarget target);
 private:
   explicit AbsoluteValue(Expression child) : Expression(TreePool::sharedPool()->createTreeNode<AbsoluteValueNode>()) {
     replaceChildAtIndexInPlace(0, child);
diff --git a/poincare/include/poincare/complex_argument.h b/poincare/include/poincare/complex_argument.h
index 014b8956d..9040a8b62 100644
--- a/poincare/include/poincare/complex_argument.h
+++ b/poincare/include/poincare/complex_argument.h
@@ -47,7 +47,7 @@ public:
   static Expression UntypedBuilder(Expression children) { return Builder(children.childAtIndex(0)); }
   static constexpr Expression::FunctionHelper s_functionHelper = Expression::FunctionHelper("arg", 1, &UntypedBuilder);
 
-  Expression shallowReduce(Context & context, Preferences::AngleUnit angleUnit);
+  Expression shallowReduce(Context & context, Preferences::AngleUnit angleUnit, ExpressionNode::ReductionTarget target);
 private:
   explicit ComplexArgument(Expression child) : Expression(TreePool::sharedPool()->createTreeNode<ComplexArgumentNode>()) {
     replaceChildAtIndexInPlace(0, child);
diff --git a/poincare/include/poincare/imaginary_part.h b/poincare/include/poincare/imaginary_part.h
index 8b40bfdd8..80da8e387 100644
--- a/poincare/include/poincare/imaginary_part.h
+++ b/poincare/include/poincare/imaginary_part.h
@@ -50,7 +50,7 @@ public:
   static Expression UntypedBuilder(Expression children) { return Builder(children.childAtIndex(0)); }
   static constexpr Expression::FunctionHelper s_functionHelper = Expression::FunctionHelper("im", 1, &UntypedBuilder);
 
-  Expression shallowReduce(Context & context, Preferences::AngleUnit angleUnit);
+  Expression shallowReduce(Context & context, Preferences::AngleUnit angleUnit, ExpressionNode::ReductionTarget target);
 private:
   explicit ImaginaryPart(Expression child) : Expression(TreePool::sharedPool()->createTreeNode<ImaginaryPartNode>()) {
     replaceChildAtIndexInPlace(0, child);
diff --git a/poincare/include/poincare/real_part.h b/poincare/include/poincare/real_part.h
index e719175cd..f1d99b93d 100644
--- a/poincare/include/poincare/real_part.h
+++ b/poincare/include/poincare/real_part.h
@@ -50,7 +50,7 @@ public:
   static Expression UntypedBuilder(Expression children) { return Builder(children.childAtIndex(0)); }
   static constexpr Expression::FunctionHelper s_functionHelper = Expression::FunctionHelper("re", 1, &UntypedBuilder);
 
-  Expression shallowReduce(Context & context, Preferences::AngleUnit angleUnit);
+  Expression shallowReduce(Context & context, Preferences::AngleUnit angleUnit, ExpressionNode::ReductionTarget target);
 private:
   explicit RealPart(Expression child) : Expression(TreePool::sharedPool()->createTreeNode<RealPartNode>()) {
     replaceChildAtIndexInPlace(0, child);
diff --git a/poincare/src/absolute_value.cpp b/poincare/src/absolute_value.cpp
index 0270ba146..4e2655683 100644
--- a/poincare/src/absolute_value.cpp
+++ b/poincare/src/absolute_value.cpp
@@ -3,6 +3,7 @@
 #include <poincare/serialization_helper.h>
 #include <poincare/simplification_helper.h>
 #include <poincare/absolute_value_layout.h>
+#include <poincare/multiplication.h>
 #include <assert.h>
 #include <cmath>
 
@@ -25,7 +26,7 @@ int AbsoluteValueNode::serialize(char * buffer, int bufferSize, Preferences::Pri
 }
 
 Expression AbsoluteValueNode::shallowReduce(Context & context, Preferences::AngleUnit angleUnit, ReductionTarget target) {
-  return AbsoluteValue(this).shallowReduce(context, angleUnit);
+  return AbsoluteValue(this).shallowReduce(context, angleUnit, target);
 }
 
 Expression AbsoluteValue::setSign(ExpressionNode::Sign s, Context * context, Preferences::AngleUnit angleUnit) {
@@ -33,12 +34,11 @@ Expression AbsoluteValue::setSign(ExpressionNode::Sign s, Context * context, Pre
   return *this;
 }
 
-Expression AbsoluteValue::shallowReduce(Context & context, Preferences::AngleUnit angleUnit) {
+Expression AbsoluteValue::shallowReduce(Context & context, Preferences::AngleUnit angleUnit, ExpressionNode::ReductionTarget target) {
   Expression e = Expression::defaultShallowReduce(context, angleUnit);
   if (e.isUndefined()) {
     return e;
   }
-  Expression c = childAtIndex(0);
 #if MATRIX_EXACT_REDUCING
 #if 0
   if (c->type() == Type::Matrix) {
@@ -46,14 +46,11 @@ Expression AbsoluteValue::shallowReduce(Context & context, Preferences::AngleUni
   }
 #endif
 #endif
-  if (c.sign(&context, angleUnit) == ExpressionNode::Sign::Positive) {
-    replaceWithInPlace(c);
-    return c;
-  }
-  if (c.sign(&context, angleUnit) == ExpressionNode::Sign::Negative) {
-    Expression result = c.setSign(ExpressionNode::Sign::Positive, &context, angleUnit);
-    replaceWithInPlace(result);
-    return result;
+  Expression c = childAtIndex(0);
+  Expression norm = c.complexNorm(context, angleUnit);
+  if (!norm.isUninitialized()) {
+    replaceWithInPlace(norm);
+    return norm.deepReduce(context, angleUnit, target);
   }
   return *this;
 }
diff --git a/poincare/src/complex_argument.cpp b/poincare/src/complex_argument.cpp
index c7d6d0396..01893996b 100644
--- a/poincare/src/complex_argument.cpp
+++ b/poincare/src/complex_argument.cpp
@@ -22,7 +22,7 @@ int ComplexArgumentNode::serialize(char * buffer, int bufferSize, Preferences::P
 }
 
 Expression ComplexArgumentNode::shallowReduce(Context & context, Preferences::AngleUnit angleUnit, ReductionTarget target) {
-  return ComplexArgument(this).shallowReduce(context, angleUnit);
+  return ComplexArgument(this).shallowReduce(context, angleUnit, target);
 }
 
 template<typename T>
@@ -30,19 +30,24 @@ Complex<T> ComplexArgumentNode::computeOnComplex(const std::complex<T> c, Prefer
   return Complex<T>(std::arg(c));
 }
 
-Expression ComplexArgument::shallowReduce(Context & context, Preferences::AngleUnit angleUnit) {
+Expression ComplexArgument::shallowReduce(Context & context, Preferences::AngleUnit angleUnit, ExpressionNode::ReductionTarget target) {
   {
     Expression e = Expression::defaultShallowReduce(context, angleUnit);
     if (e.isUndefined()) {
       return e;
     }
   }
-#if MATRIX_EXACT_REDUCING
   Expression c = childAtIndex(0);
+#if MATRIX_EXACT_REDUCING
   if (c.type() == ExpressionNode::Type::Matrix) {
     return SimplificationHelper::Map(*this, context, angleUnit);
   }
 #endif
+  Expression arg = c.complexArgument(context, angleUnit);
+  if (!arg.isUninitialized()) {
+    replaceWithInPlace(arg);
+    return arg.deepReduce(context, angleUnit, target);
+  }
   return *this;
 }
 
diff --git a/poincare/src/expression_node.cpp b/poincare/src/expression_node.cpp
index cc5c0432f..9541ee766 100644
--- a/poincare/src/expression_node.cpp
+++ b/poincare/src/expression_node.cpp
@@ -109,7 +109,7 @@ Expression ExpressionNode::complexArgument(Context & context, Preferences::Angle
           Multiplication(
             SignFunction::Builder(b).shallowReduce(context, angleUnit),
             Division(Constant(Ion::Charset::SmallPi), Rational(2)).shallowReduce(context, angleUnit, ReductionTarget::BottomUpComputation)
-          ),
+          ).shallowReduce(context, angleUnit, ReductionTarget::BottomUpComputation),
           arcTangent
         ).shallowReduce(context, angleUnit, ReductionTarget::BottomUpComputation);
     } else {
diff --git a/poincare/src/imaginary_part.cpp b/poincare/src/imaginary_part.cpp
index 2a5c3ae43..9379d5ec4 100644
--- a/poincare/src/imaginary_part.cpp
+++ b/poincare/src/imaginary_part.cpp
@@ -20,10 +20,10 @@ int ImaginaryPartNode::serialize(char * buffer, int bufferSize, Preferences::Pri
 }
 
 Expression ImaginaryPartNode::shallowReduce(Context & context, Preferences::AngleUnit angleUnit, ReductionTarget target) {
-  return ImaginaryPart(this).shallowReduce(context, angleUnit);
+  return ImaginaryPart(this).shallowReduce(context, angleUnit, target);
 }
 
-Expression ImaginaryPart::shallowReduce(Context & context, Preferences::AngleUnit angleUnit) {
+Expression ImaginaryPart::shallowReduce(Context & context, Preferences::AngleUnit angleUnit, ExpressionNode::ReductionTarget target) {
   {
     Expression e = Expression::defaultShallowReduce(context, angleUnit);
     if (e.isUndefined()) {
@@ -41,6 +41,11 @@ Expression ImaginaryPart::shallowReduce(Context & context, Preferences::AngleUni
     replaceWithInPlace(result);
     return result;
   }
+  Expression im = c.imaginaryPart(context, angleUnit);
+  if (!im.isUninitialized()) {
+    replaceWithInPlace(im);
+    return im.deepReduce(context, angleUnit, target);
+  }
   return *this;
 }
 
diff --git a/poincare/src/real_part.cpp b/poincare/src/real_part.cpp
index b4fdf9e88..e599dce38 100644
--- a/poincare/src/real_part.cpp
+++ b/poincare/src/real_part.cpp
@@ -20,10 +20,10 @@ int RealPartNode::serialize(char * buffer, int bufferSize, Preferences::PrintFlo
 }
 
 Expression RealPartNode::shallowReduce(Context & context, Preferences::AngleUnit angleUnit, ReductionTarget target) {
-  return RealPart(this).shallowReduce(context, angleUnit);
+  return RealPart(this).shallowReduce(context, angleUnit, target);
 }
 
-Expression RealPart::shallowReduce(Context & context, Preferences::AngleUnit angleUnit) {
+Expression RealPart::shallowReduce(Context & context, Preferences::AngleUnit angleUnit, ExpressionNode::ReductionTarget target) {
   {
     Expression e = Expression::defaultShallowReduce(context, angleUnit);
     if (e.isUndefined()) {
@@ -40,6 +40,11 @@ Expression RealPart::shallowReduce(Context & context, Preferences::AngleUnit ang
     replaceWithInPlace(c);
     return c;
   }
+  Expression re = c.realPart(context, angleUnit);
+  if (!re.isUninitialized()) {
+    replaceWithInPlace(re);
+    return re.deepReduce(context, angleUnit, target);
+  }
   return *this;
 }
 
diff --git a/poincare/test/complex.cpp b/poincare/test/complex.cpp
index d47451641..e86e56afb 100644
--- a/poincare/test/complex.cpp
+++ b/poincare/test/complex.cpp
@@ -69,12 +69,12 @@ QUIZ_CASE(poincare_complex_parts) {
   assert_expression_has_complex_cartesian_parts("I", "0", "1");
 
   assert_expression_has_complex_cartesian_parts("abs(-3)", "3", "0");
-  assert_expression_has_complex_cartesian_parts("abs(-3+I)", "abs(-3+I)", "0");
+  assert_expression_has_complex_cartesian_parts("abs(-3+I)", "R(10)", "0");
   assert_expression_has_complex_cartesian_parts("atan(2)", "atan(2)", "0");
   assert_expression_has_complex_cartesian_parts("atan(2+I)", nullptr, nullptr);
   assert_expression_has_complex_cartesian_parts("binomial(10, 4)", "210", "0");
   assert_expression_has_complex_cartesian_parts("ceil(-1.3)", "-1", "0");
-  assert_expression_has_complex_cartesian_parts("arg(-2)", "arg(-2)", "0");
+  assert_expression_has_complex_cartesian_parts("arg(-2)", "P", "0");
   // TODO: confidence is not simplified yet
   //assert_expression_has_complex_cartesian_parts("confidence(-2,-3)", "confidence(-2)", "0");
   assert_expression_has_complex_cartesian_parts("conj(-2)", "-2", "0");
@@ -87,7 +87,7 @@ QUIZ_CASE(poincare_complex_parts) {
   assert_expression_has_complex_cartesian_parts("floor(x)", "floor(x)", "0");
   assert_expression_has_complex_cartesian_parts("frac(x)", "frac(x)", "0");
   assert_expression_has_complex_cartesian_parts("gcd(x,y)", "gcd(x,y)", "0");
-  assert_expression_has_complex_cartesian_parts("im(x)", "im(x)", "0");
+  assert_expression_has_complex_cartesian_parts("im(1+I)", "1", "0");
   assert_expression_has_complex_cartesian_parts("int(x^2, x, 1, 2)", "int(x^2,x,1,2)", "0");
   assert_expression_has_complex_cartesian_parts("lcm(x,y)", "lcm(x,y)", "0");
   // TODO: dim is not simplified yet
@@ -101,7 +101,7 @@ QUIZ_CASE(poincare_complex_parts) {
   //assert_expression_has_complex_cartesian_parts("prediction(-2,-3)", "prediction(-2)", "0");
   assert_expression_has_complex_cartesian_parts("randint(2,4)", "randint(2,4)", "0");
   assert_expression_has_complex_cartesian_parts("random()", "random()", "0");
-  assert_expression_has_complex_cartesian_parts("re(x)", "re(x)", "0");
+  assert_expression_has_complex_cartesian_parts("re(x)", "x", "0");
   assert_expression_has_complex_cartesian_parts("round(x,y)", "round(x,y)", "0");
   assert_expression_has_complex_cartesian_parts("sign(x)", "sign(x)", "0");
   assert_expression_has_complex_cartesian_parts("sin(23)", "sin(23)", "0");
@@ -148,5 +148,5 @@ QUIZ_CASE(poincare_complex_parts) {
   assert_expression_has_complex_polar_parts("P", "P", "0");
   assert_expression_has_complex_polar_parts("I", "1", "P/2");
   assert_expression_has_complex_polar_parts("abs(-3)", "3", "0");
-  assert_expression_has_complex_polar_parts("abs(-3+I)", "abs(-3+I)", "0");
+  assert_expression_has_complex_polar_parts("abs(-3+I)", "R(10)", "0");
 }
diff --git a/poincare/test/function.cpp b/poincare/test/function.cpp
index 8c711a7b5..d8d9d654a 100644
--- a/poincare/test/function.cpp
+++ b/poincare/test/function.cpp
@@ -238,6 +238,8 @@ QUIZ_CASE(poincare_function_evaluate) {
 QUIZ_CASE(poincare_function_simplify) {
   assert_parsed_expression_simplify_to("abs(P)", "P");
   assert_parsed_expression_simplify_to("abs(-P)", "P");
+  assert_parsed_expression_simplify_to("abs(1+I)", "R(2)");
+  assert_parsed_expression_simplify_to("arg(1+I)", "P/4");
   assert_parsed_expression_simplify_to("binomial(20,3)", "1140");
   assert_parsed_expression_simplify_to("binomial(20,10)", "184756");
   assert_parsed_expression_simplify_to("ceil(-1.3)", "-1");
@@ -257,9 +259,11 @@ QUIZ_CASE(poincare_function_simplify) {
   assert_parsed_expression_simplify_to("frac(-1.3)", "7/10");
   assert_parsed_expression_simplify_to("gcd(123,278)", "1");
   assert_parsed_expression_simplify_to("gcd(11,121)", "11");
+  assert_parsed_expression_simplify_to("im(1+5*I)", "5");
   assert_parsed_expression_simplify_to("lcm(123,278)", "34194");
   assert_parsed_expression_simplify_to("lcm(11,121)", "121");
   assert_parsed_expression_simplify_to("R(4)", "2");
+  assert_parsed_expression_simplify_to("re(1+5*I)", "1");
   assert_parsed_expression_simplify_to("root(4,3)", "root(4,3)");
   assert_parsed_expression_simplify_to("root(4,P)", "4^(1/P)");
   assert_parsed_expression_simplify_to("root(27,3)", "3");