MHB S10.03.25 Write complex number in rectangular form

[karush]

$\tiny{s10.03.25}$
$\textsf{Write complex number in rectangular form}$
\begin{align*}\displaystyle
z&=4\left[\cos\frac{7\pi}{4} + i\sin \frac{7\pi}{4} \right]\\
\end{align*}
$\textit{ok from the unit circle: $\displaystyle\cos{\left(\frac{7\pi}{4}\right)}=\frac{\sqrt{2}}{2}$}\\$
$\textit{and it appears distributing in 4 gives the answer}\\$
$\textit{but isn't the purpose of this to deal with powers?}\\$

$\textit{book answer} =2\sqrt{2}+2\sqrt{2}i$

$\textit{however $W|A$ returned $-1$ ??}$

 

[Greg]

$$\sin\left(\frac{7\pi}{4}\right)=-\frac{\sqrt2}{2}$$

The correct answer is $2\sqrt2-2\sqrt2i$.

Double-check what you entered into W|A.

 

[karush]

ok the $i$ confuses me

 

[Greg]

It is merely the coefficient of the sine function. Why are you confused? Because $i=\sqrt{-1}$?