Question

convert each of the complex number in √3+i​

Answer 1

Answer:

ANSWER

1−3i

2

−16(1−i

3

)

=8(

2

−1

+

2

3

)=8(cos

3

2π

+isin

3

2π

)=8e

i

3

2π

Step-by-step explanation:

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Answer 2

Given :-

Convert each of the complex numbers given in the Exercise 3 to 8 in the polar form:

$\sqrt{3 + i}$

$z = \sqrt{3 + i}$

$r = |z | = \sqrt{( \sqrt{3) {}^{2} } } + (1) {}^{2} = \sqrt{3 + 1 = 2}$

Let ∅

$= tan { }^{ - 1} | \frac{y}{x} | = tan {}^{ - 1} | \frac{1}{ \sqrt{3} } | = \frac{\pi}{6}$

Since Z Lies in 1 Quadrant.

So, arg ument of = ( ∅ ) = ∅

$= \frac{\pi}{6}$

Therefor Z = r ( Cos ø + I sin ∅ )

$= 2(cos \frac{\pi}{6} + i \: sin \frac{\pi}{6} )$

The System Is Solved ✔️.