Question

PLS HELP WILL GIVE BRAINLIST - Which number represents a square root of 3 (cosine (StartFraction pi Over 2 EndFraction) + I sine (StartFraction pi Over 2 EndFraction) )?

Answer 1

Answer:

B

Step-by-step explanation:

Got it right on the test

Answer 2

(B) $\sqrt{3} (cos(\frac{\pi }{4} )+i sin(\frac{\pi }{4} ))$

Square root:

• The factor we can multiply by itself to obtain a given number is the number's square root.
• Sqrt, which stands for "square root of," is the sign for the term.
• Squaring an integer is the reverse of finding its square root.

Steps to square root a trigonometric function -

1. Find the given trigonometric equation.
2. Put the square term on its own side of the equal sign.
3. Taking square roots on both sides.
4. By using inverse trigonometric functions, get the value of x.

Explanation:

De Moivre's theorem: $z=r*[cos($θ$)+i*sin($θ$)}$$]$

Raising both sides to the $n^{th}$ - $z^{n} =r^{n} *[cos(n*$θ$)+i*sin(n*$θ$)]$

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

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

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

Therefore, the correct answer to the question is (B) $\sqrt{3} (cos(\frac{\pi }{4} )+i sin(\frac{\pi }{4} ))$.

Know more about square roots here:

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