Question

Express the complex number in trigonometric form. 5 - 5i

Answer 1

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               Hi my lil bunny!

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Lets do this step by step.

This is the trigonometric form of a complex number where $|z|$ is the modulus and $0$ is the angle created on the complex plane.

$z = a + bi = |z| (cos ( 0 ) + I sin (0))$

The modulus of a complex number is the distance from the origin on the complex plane.

$|z| = \sqrt{a^2 + b^2}$ where $z = a + bi$

Substitute the actual values of a = -5 and b = -5.

$|z| = \sqrt{(-5) ^2 + (-5) ^2}$

Now Find $|z|$ .

Raise - 5 to the power of 2.

$|z| = \sqrt{25 + (-5) ^2}$

Raise - 5 to the power of 2.

$|z| = \sqrt{25 + 25}$

Add 25 and 25.

$|z| = \sqrt{50}$

Rewrite 50 as 5^2 . 2 .

$|z| = 5\sqrt{2}$

Pull terms out from under the radical.

$|z| = 5\sqrt{2}$

The angle of the point on the complex plane is the inverse tangent of the complex portion over the real portion.

$0 = arctan (\frac{-5}{-5} )$

Since inverse tangent of  $\frac{-5}{-5}$  produces an angle in the third quadrant, the value of the angle is $\frac{5\pi }{4}$ .

$0 = \frac{5\pi }{4}$

Substitute the values of $0 = \frac{5\pi }{4}$ and $|z| = 5\sqrt{2}$ .

$5\sqrt{2} ( cos( \frac{5\pi}{4}) + i sin (\frac{5\pi}{4}))$

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●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀

Answer 2

Answer:

five square root two times the quantity cosine of five pi divided by four plus i times sine of five pi divided by four