Question

Convert each of the complex numbers given in in the polar form: 5.- 1-i
​

Answer 1

Answer:

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=−4π    (As θ lies in fourth quadrant.)

So, the polar form is 

∴1−i=rcosθ+irsinθ=2cos(4−π)+i2sin(4−π)

=2[cos(4−π)+isin(