Question

convert complex number given in the polar form:-1+i​

Answer 1

Answer:

Step-by-step explanation:

Gn: z=-1+i

Polar form = r[cos theta + i*sin theta]

By Comparing both sides,

Let r*cos theta = -1

r*i* sin theta = i

r*sin theta = 1

r = |z| = |-1+i|

$=\sqrt{(-1)^{2} + 1^{2} } = \sqrt{1+1} = \sqrt{2}\\r = \sqrt{2}$

r cos theta = -1

cos theta = -1/$\sqrt{2}$

cos theta(180 - 45) = -1/$\sqrt{2}$

-cos theta = -1/$\sqrt{2}$

theta = 45

Therefore the polar form is $\sqrt{2}$(cos 45 + i sin 45)

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