Mathematics: Which number represents a square root of 3 [cos(pi/2) + i sin (pi/2)]?

Which number represents a square root of 3 [cos(pi/2)

Ответ:

tanviknawale

27.11.2021

Mathematics

Choice B

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Explanation:

We use De Moivre's Theorem. It says that if you started with

$z = r*\left[\cos\left(\theta\right)+i*\sin\left(\theta\right)\right]$

then raising both sides to the nth power leads to

$z^n = r^n*\left[\cos\left(n*\theta\right)+i*\sin\left(n*\theta\right)\right]$

The term out front r is raised to the nth power. We also have copies of n inside the trig functions.

The square root operation undoes the squaring operation, so we'll be dealing with n = 2.

If you were to go through each answer choice, then you'll find that squaring choice B will lead to the original expression given.

$z = \sqrt{3}*\left[\cos\left(\frac{\pi}{4}\right)+i*\sin\left(\frac{\pi}{4}\right)\right]\\\\\\z^2 = (\sqrt{3})^2*\left[\cos\left(2*\frac{\pi}{4}\right)+i*\sin\left(2*\frac{\pi}{4}\right)\right]\\\\\\z^2 = 3*\left[\cos\left(\frac{\pi}{2}\right)+i*\sin\left(\frac{\pi}{2}\right)\right]\\\\\\$

Note that working this process in reverse means we apply the square root and we'll go from the expression in choice B to the original expression again.

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Ответ:

aurelio1121

15.08.2021

Mathematics

$\sqrt{x}$ -1

Step-by-step explanation:

simplified into words. lol

Plz mark me brainliest!

It's ok if u don't...lol

I hope this helped!!

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Which number represents a square root of 3 [cos(pi/2) + i sin (pi/2)]?

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