1. ## Euler form

Hi,

Q1. Simplify the following, working by hand Give the answers in the form a+bi with a and b exact real numbers, not decimal approximations.

[squareroot(2) - i*squareroot(2)]^10 (use euler form)

If there is anything unclear, let me know, thanks in advance.

2. Originally Posted by Moon Hoplite
Hi,

Q1. Simplify the following, working by hand Give the answers in the form a+bi with a and b exact real numbers, not decimal approximations.

[squareroot(2) - i*squareroot(2)]^10 (use euler form)

$= (\sqrt{2})^{10} (1 - i)^{10}$.
Convert $1 - i$ to polar form and get $(1 - i)^{10}$ using de Moivre's theorem. Then convert the result into Cartesian form.