Question 1404b

Complex Numbers

Conversion from Modulus-Argument to Cartesian Form

Question

The complex number

{z}

is given by

z={\textstyle 2 \left( \cos \left( - \frac{1}{4} \pi \right) + \mathrm{i} \sin \left( - \frac{1}{4} \pi \right) \right).}

Find

{z}

in cartesian form

{x + \mathrm{i}y,}

where

{x, y \in \mathbb{R}.}

{x = }

{y = }