Given, z=1−i
Let rcosθ=1andrsinθ=−1
On squaring and adding, we obtain
r2cos2θ+r2sin2θ=12+(−1)2
⇒r2(cos2θ+sin2θ)=2
⇒r2=2
⇒r=√2 (since,r>0 )
∴√2cosθ=1 and √2sinθ=−1
∴θ=−π4 (As θ lies in fourth quadrant.)
So, the polar form is
∴1−i=rcosθ+irsinθ=√2cos(−π4)+i√2sin(−π4)
=√2[cos(−π4)+isin(−π4)]