Question

Convert in the polar form 1+7i/(1-3i)2.

Answer 1

i) Here, z=(2−i)21+7i

=4+i2−4i1+7i

=4−1−4i1+7i

=3−4i1+7i×3+4i3+4i

=32+423+4i+21i+28i2

=32+423+4i+21i−28=25−25+25i

=−1+i

Let rcosθ=−1 and rsinθ=1

On squaring and adding, we obtain

r2(cos2θ+sin2θ)=1+1

⇒r2(cos2θ+sin2θ)=2

⇒