Answer:
[tex]10e^{i\frac{7\pi}{4}}[/tex]
Step-by-step explanation:
The magnitude of the number is ...
[tex]|5\sqrt{2}-5i\sqrt{2}|=\sqrt{(5\sqrt{2})^2+(-5\sqrt{2})^2}=\sqrt{50+50}=10[/tex]
The angle of the number is in the 4th quadrant:
[tex]\arctan{\dfrac{-5\sqrt{2}}{5\sqrt{2}}}=\arctan{(-1)}=\dfrac{7\pi}{4}[/tex]
So, the exponential form of the number is ...
[tex]\boxed{10e^{i\frac{7\pi}{4}}}[/tex]
