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Question

Convert the given complex number in polar form: -3

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Solution

z = -3
Let rcosθ=3 and rsinθ=0
On squaring and adding, we obtain
r2cos2θ+r2sin2θ=(3)2r2(cos2θ+sin2θ)=9r2=9r=9=3 [Conventionally, r>0]3 cosθ=3 and 3 sinθ=0cosθ=1 and sinθ=0θ=π3=r cosθ+i rsinθ=3 cosπ+i 3 sinπ=3(cosπ+i sinπ)
This is the required polar form.


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