ComplexExpand

ComplexExpand[e] returns a complex expansion of e.

Attributes[ComplexExpand] := {Protected}

Simple examples

In[1]:= ComplexExpand[a]
Out[1]= a

In[2]:= ComplexExpand[1]
Out[2]= 1

In[3]:= ComplexExpand[a*(b + c)]
Out[3]= a*b + a*c

In[4]:= ComplexExpand[-1^(1)/(3)]
Out[4]= (1)/(2) + (I*Sqrt[3])/(2)

In[5]:= ComplexExpand[-1^(4)/(3)]
Out[5]= (1)/(2)*-1 + ((I*Sqrt[3]))/(2)*-1

In[6]:= ComplexExpand[2^(4)/(3)]
Out[6]= 2*2^(1)/(3)

In[7]:= ComplexExpand[-1^(1)/(3)*(1 + I*Sqrt[3])]
Out[7]= -1 + I*Sqrt[3]

In[8]:= ComplexExpand[d*E^((a + I*b)*c)]
Out[8]= d*E^(a*c)*Cos[b*c] + d*I*E^(a*c)*Sin[b*c]

In[9]:= ComplexExpand[(1*E^(I*(Pi)/(4)))/(2)]
Out[9]= ((1)/(2) + (I)/(2))/(Sqrt[2])