Question

Write a complex number in trigonometric form, using the degree measure for the argument:
-5sqrt(2)+5i sqrt(2)

Answer 1

Answer on Question #52712 – Math – Complex Analysis

Write a complex number in trigonometric form, using the degree measure for the argument:

$$-5\sqrt{2} + 5i\sqrt{2}$$

Solution

Let's rewrite the given complex number as follows

$$-5\sqrt{2} + 5i\sqrt{2} = 10\left(-\frac{1}{\sqrt{2}} + i\frac{1}{\sqrt{2}}\right) = 10\left(\cos\frac{3\pi}{4} + i\sin\frac{3\pi}{4}\right)$$

**Answer**: $10\left(\cos\frac{3\pi}{4} + i\sin\frac{3\pi}{4}\right)$.

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