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Question

Convert the complex number z=-1-i in to the polar form.

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Solution

Here z=1i=r(cos θ+i sin θ)

r cos θ=1 and r sin θ=1 i

Squaring both sides of (i) and adding

r2(cos2 θ+sin2 θ)=1+1

r2=2 r=2

2 cos θ=1 and 2sin θ=1

cos θ=12 and sin θ=12

Since sin θ and cos θ are both negative

θ lies in third quadrant

θ=(π+π4)=3π4

Hence polar form of z is

2[cos(3π4)+i sin(3π4)].


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