Question

convert 1+iroot3 divided by 2 into polar form​

Answer 1

Step-by-step explanation:

1+root3/2

=1/2+root3/2

0.5+0.8660254038

1.3660254038

Answer 2

$cos\frac{\pi}{3}+isin\frac{\pi}{3}$

Step-by-step explanation:

Let $a+ib=\frac{1+i\sqrt3 }{2}=\frac{1}{2}+i\frac{\sqrt 3}{2}$

Comparing on both sides we get

$a=\frac{1}{2}$

$b=\frac{\sqrt 3}{2}$

$r=\sqrt{a^2+b^2}=\sqrt{(\frac{1}{2})^2+(\frac{\sqrt3 }{2})^2}=1$

$tan\theta=\mid\frac{b}{a}\mid$

Using the formula

$tan\theta=\mid \frac{\frac{\sqrt 3}{2}}{\frac{1}{2}}\mid=\sqrt 3$

$tan\theta=tan\frac{\pi}{3}$

$\theta=\frac{\pi}{3}$

Polar form of a+ib is given by

$r(cos\theta+isin\theta)$

Using the formula

Polar form: $cos\frac{\pi}{3}+isin\frac{\pi}{3}$

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