Expressions involving complex numbers

Question

A question on my homework is as follows:

e^(ln(3)+(π/2)i) * (2π/3)^3 - 3π/3

The question states "Solve and simplify as much as possible. Give the answer in rectangular coordinates (in the form 𝑥 + 𝑦𝑖) and in polar coordinates (in the form 𝑟𝜃).

Most online calculators have failed at solving, much less explaining, this so any help would be appreciated.

Answer 1

e^{ln3 + (π/2)i} = e^ln3e^(π/2)i = 3[cos(π/2) + isin(π/2)] = 3i

Does that help?