diff --git a/poincare/include/poincare/conjugate.h b/poincare/include/poincare/conjugate.h
index 4c96ccecc..7c36ee9cc 100644
--- a/poincare/include/poincare/conjugate.h
+++ b/poincare/include/poincare/conjugate.h
@@ -18,6 +18,7 @@ public:
   }
 #endif
 
+  bool isReal(Context & context, Preferences::AngleUnit angleUnit) const override { return childAtIndex(0)->isReal(context, angleUnit); }
   ComplexCartesian complexCartesian(Context & context, Preferences::AngleUnit angleUnit) const override;
   ComplexPolar complexPolar(Context & context, Preferences::AngleUnit angleUnit) const override;
 
@@ -46,7 +47,7 @@ public:
   static Expression UntypedBuilder(Expression children) { return Builder(children.childAtIndex(0)); }
   static constexpr Expression::FunctionHelper s_functionHelper = Expression::FunctionHelper("conj", 1, &UntypedBuilder);;
 
-  Expression shallowReduce(Context & context, Preferences::AngleUnit angleUnit);
+  Expression shallowReduce(Context & context, Preferences::AngleUnit angleUnit, ExpressionNode::ReductionTarget target);
 private:
   explicit Conjugate(Expression child) : Expression(TreePool::sharedPool()->createTreeNode<ConjugateNode>()) {
     replaceChildAtIndexInPlace(0, child);
diff --git a/poincare/include/poincare/function.h b/poincare/include/poincare/function.h
index 95a57169b..aecee8ad5 100644
--- a/poincare/include/poincare/function.h
+++ b/poincare/include/poincare/function.h
@@ -28,6 +28,7 @@ public:
   float characteristicXRange(Context & context, Preferences::AngleUnit angleUnit) const override;
 
   // Complex
+  bool isReal(Context & context, Preferences::AngleUnit angleUnit) const override;
   ComplexCartesian complexCartesian(Context & context, Preferences::AngleUnit angleUnit) const override;
   ComplexPolar complexPolar(Context & context, Preferences::AngleUnit angleUnit) const override;
 
diff --git a/poincare/include/poincare/symbol.h b/poincare/include/poincare/symbol.h
index ec529e55a..989bfef8f 100644
--- a/poincare/include/poincare/symbol.h
+++ b/poincare/include/poincare/symbol.h
@@ -27,6 +27,7 @@ public:
   float characteristicXRange(Context & context, Preferences::AngleUnit angleUnit) const override;
 
   // Complex
+  bool isReal(Context & context, Preferences::AngleUnit angleUnit) const override;
   ComplexCartesian complexCartesian(Context & context, Preferences::AngleUnit angleUnit) const override;
   ComplexPolar complexPolar(Context & context, Preferences::AngleUnit angleUnit) const override;
 
diff --git a/poincare/include/poincare/symbol_abstract.h b/poincare/include/poincare/symbol_abstract.h
index 97a264760..e5ffb9c2c 100644
--- a/poincare/include/poincare/symbol_abstract.h
+++ b/poincare/include/poincare/symbol_abstract.h
@@ -80,6 +80,7 @@ protected:
   SymbolAbstractNode * node() const { return static_cast<SymbolAbstractNode *>(Expression::node()); }
 private:
   static Expression Expand(const SymbolAbstract & symbol, Context & context, bool clone);
+  static bool isReal(const SymbolAbstract & symbol, Context & context, Preferences::AngleUnit angleUnit);
   static ComplexCartesian complexCartesian(const SymbolAbstract & symbol, Context & context, Preferences::AngleUnit angleUnit);
   static ComplexPolar complexPolar(const SymbolAbstract & symbol, Context & context, Preferences::AngleUnit angleUnit);
   static size_t AlignedNodeSize(size_t nameLength, size_t nodeSize);
diff --git a/poincare/src/conjugate.cpp b/poincare/src/conjugate.cpp
index 1ee35cf23..eae04b0ac 100644
--- a/poincare/src/conjugate.cpp
+++ b/poincare/src/conjugate.cpp
@@ -47,7 +47,7 @@ int ConjugateNode::serialize(char * buffer, int bufferSize, Preferences::PrintFl
 }
 
 Expression ConjugateNode::shallowReduce(Context & context, Preferences::AngleUnit angleUnit, ReductionTarget target) {
-  return Conjugate(this).shallowReduce(context, angleUnit);
+  return Conjugate(this).shallowReduce(context, angleUnit, target);
 }
 
 template<typename T>
@@ -55,7 +55,7 @@ Complex<T> ConjugateNode::computeOnComplex(const std::complex<T> c, Preferences:
   return Complex<T>(std::conj(c));
 }
 
-Expression Conjugate::shallowReduce(Context & context, Preferences::AngleUnit angleUnit) {
+Expression Conjugate::shallowReduce(Context & context, Preferences::AngleUnit angleUnit, ExpressionNode::ReductionTarget target) {
   {
     Expression e = Expression::defaultShallowReduce(context, angleUnit);
     if (e.isUndefined()) {
@@ -68,6 +68,18 @@ Expression Conjugate::shallowReduce(Context & context, Preferences::AngleUnit an
     return SimplificationHelper::Map(*this, context, angleUnit);
   }
 #endif
+  if (c.isReal(context, angleUnit)) {
+    replaceWithInPlace(c);
+    return c;
+  }
+  if (c.type() == ExpressionNode::Type::ComplexCartesian) {
+    ComplexCartesian complexChild = static_cast<ComplexCartesian &>(c);
+    Multiplication m(Rational(-1), complexChild.imag());
+    complexChild.replaceChildAtIndexInPlace(1, m);
+    m.shallowReduce(context, angleUnit, target);
+    replaceWithInPlace(complexChild);
+    return complexChild;
+  }
   if (c.type() == ExpressionNode::Type::Rational) {
     replaceWithInPlace(c);
     return c;
diff --git a/poincare/src/function.cpp b/poincare/src/function.cpp
index 9103f4a85..2d6346f9f 100644
--- a/poincare/src/function.cpp
+++ b/poincare/src/function.cpp
@@ -14,6 +14,11 @@ ComplexCartesian FunctionNode::complexCartesian(Context & context, Preferences::
   return SymbolAbstract::complexCartesian(f, context, angleUnit);
 }
 
+bool FunctionNode::isReal(Context & context, Preferences::AngleUnit angleUnit) const {
+  Function f(this);
+  return SymbolAbstract::isReal(f, context, angleUnit);
+}
+
 ComplexPolar FunctionNode::complexPolar(Context & context, Preferences::AngleUnit angleUnit) const {
   Function f(this);
   return SymbolAbstract::complexPolar(f, context, angleUnit);
diff --git a/poincare/src/symbol.cpp b/poincare/src/symbol.cpp
index 1e171fe8d..754f558cc 100644
--- a/poincare/src/symbol.cpp
+++ b/poincare/src/symbol.cpp
@@ -77,6 +77,11 @@ float SymbolNode::characteristicXRange(Context & context, Preferences::AngleUnit
   return 0.0f;
 }
 
+bool SymbolNode::isReal(Context & context, Preferences::AngleUnit angleUnit) const {
+  Symbol s(this);
+  return SymbolAbstract::isReal(s, context, angleUnit);
+}
+
 ComplexCartesian SymbolNode::complexCartesian(Context & context, Preferences::AngleUnit angleUnit) const {
   Symbol s(this);
   return SymbolAbstract::complexCartesian(s, context, angleUnit);
diff --git a/poincare/src/symbol_abstract.cpp b/poincare/src/symbol_abstract.cpp
index faea41a33..c8f57e0c9 100644
--- a/poincare/src/symbol_abstract.cpp
+++ b/poincare/src/symbol_abstract.cpp
@@ -80,6 +80,14 @@ Expression SymbolAbstract::Expand(const SymbolAbstract & symbol, Context & conte
   return e;
 }
 
+bool SymbolAbstract::isReal(const SymbolAbstract & symbol, Context & context, Preferences::AngleUnit angleUnit) {
+  Expression e = SymbolAbstract::Expand(symbol, context, false);
+  if (e.isUninitialized()) {
+    return true;
+  }
+  return e.isReal(context, angleUnit);
+}
+
 ComplexCartesian SymbolAbstract::complexCartesian(const SymbolAbstract & symbol, Context & context, Preferences::AngleUnit angleUnit) {
   Expression e = SymbolAbstract::Expand(symbol, context, true);
   if (e.isUninitialized()) {