ComplexExpand

ComplexExpand(expr)

expands expr. All variable symbols in expr are assumed to be non complex numbers.

ComplexExpand(expr, {x1, x2, ...})

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

See

• Wikipedia - List of trigonometric identities
• Wikipedia - Complex number

Examples

Assume that both x and y are real:

>> ComplexExpand(Sin(x+I*y))
Cosh(y)*Sin(x)+I*Cos(x)*Sinh(y)

>> ComplexExpand(3^(I*x))
Cos(1/2*x*Log(9))+I*Sin(1/2*x*Log(9))

Implementation status

• ☑ - partially implemented

Github

• Implementation of ComplexExpand