Question

what is the polar form of the complex number√3+i/1-i is? ​

Answer 1

Answer:

Given complex number is 3+i

Let rcosθ=3 and rsinθ=1

On squaring and adding, we obtain 

r2cos2θ+r2sin2θ=(3)2+12

⇒r2(cos2θ+sin2θ)=3+1

⇒r2=4

⇒r=4=2  [ Conventionally, r>0]

∴2cosθ=3 and 2sinθ=1

⇒cosθ=23 and sinθ=21

∴θ=6π   [ As θ lies in the I quadrant ]

∴3+i=rcosθ+irsinθ=2cos6π+i2sin

Answer 2

Answer:

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