# Calculus II

posted by
**Becky** on
.

What is sin(i) -- (sin of the imaginary number, i)

What is cos(i)-- cosine of the imaginary number, i

orrr

tan(1+i)

You can derive these things from the equation:

Exp(i x) = cos(x) + i sin(x) --->

sin(x) = [Exp(ix) - Exp(-ix)]/(2i)

cos(x) = [Exp(ix) + Exp(-ix)]/2

tan(x) =

1/i * [Exp(ix) - Exp(-ix)]/[Exp(ix) + Exp(-ix)]

These relations are also valid for complex values for x. E.g.:

tan(1+i) =

1/i * [Exp(i-1) - Exp(-i+1)]/[Exp(i-1) + Exp(-i+1)]

Exp[i-1] = Exp[i]Exp[-1] = Exp[-1](cos(1)+isin(1))

Exp[-i+1] = Exp[-i]Exp[1] = Exp[1](cos(1)-isin(1))