How do you convert -1+i1+i to polar form?

1 Answer
May 22, 2016

Polar form of -1+i1+i is (sqrt2,(3pi)/4)(2,3π4)

Explanation:

A complex number a+iba+ib in polar form is written as

rcostheta+irsinthetarcosθ+irsinθ, costheta=a/rcosθ=ar and sintheta=b/rsinθ=br

Hence r=sqrt(a^2+b^2)r=a2+b2

As in -1+i1+i a=-1a=1 and b=1b=1

r=sqrt((-1)^2+1^2)=sqrt2r=(1)2+12=2 and hence

costheta=-1/sqrt2cosθ=12 and sintheta=1/sqrt2sinθ=12

Hence, theta=(3pi)/4θ=3π4 and

Polar form of -1+i1+i is (sqrt2,(3pi)/4)(2,3π4)