Question

I NEED HELP PLEASE, THANKS! :)

Answer 1

`10e^{i(7\pi)/(4)}`

Explanation:

The magnitude of the number is ...

`|5√(2)-5i√(2)|=\sqrt{(5√(2))^2+(-5√(2))^2}=√(50+50)=10`

The angle of the number is in the 4th quadrant:

`\arctan{(-5√(2))/(5√(2))}=\arctan{(-1)}=(7\pi)/(4)`

So, the exponential form of the number is ...

`\boxed{10e^{i(7\pi)/(4)}}`