Question

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Answer 1

Answer:

  $10e^{i\frac{7\pi}{4}}$

Step-by-step explanation:

The magnitude of the number is ...

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

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

  $\arctan{\dfrac{-5\sqrt{2}}{5\sqrt{2}}}=\arctan{(-1)}=\dfrac{7\pi}{4}$

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

  $\boxed{10e^{i\frac{7\pi}{4}}}$