• ← ArcTanh
• → Cosh

ComplexExpand

(SymPy, WMA)

ComplexExpand[expr]

expands expr assuming that all variables are real.

ComplexExpand[expr,{$x_1$,$x_2$, ...}]

expands expr assuming that variables matching any of the xi are complex.

Note: we get equivalent, but different results from WMA:

• • ComplexExpand[3^(I x)]

Assume that both x and y and are real:

• • ComplexExpand[Sin[x + I y]]

Take x to be complex:

• • ComplexExpand[Sin[x], x]

Polynomials:

• • ComplexExpand[Re[z^5 - 2 z^3 - z + 1], z]

Trigonometric and hyperbolic functions

• • ComplexExpand[Cos[x + I y] + Tanh[z], {z}]

Exponential and logarithmic functions:

• • ComplexExpand[Abs[2^z Log[2 z]], z]

Specify that variable z is taken to be complex:

• • ComplexExpand[Re[2 z^3 - z + 1], z]