Question

convert 1+2i/1-3i to polar form​

Answer 1

z = (1 + 2i)/(1 - 3i)
= (1 + 2i)(1 +3i)/(1 - 3i)(1 + 3i)
= {1(1 + 3i)+2i(1 +3i)}/{1²-(3i)²}
= ( 1 +3i +2i + 6i²)/(1 + 9)
= (-5 + 5i)/10
= (-1/2) + (1/2)i

now, modulus of the complex number is |(-1/2) + (1/2)i|
= √{(-1/2)² + (1/2)²}
= √{1/4 + 1/4}
= 1/√2

now, tan∅ = |Im(z)/Re(z)|
= |(1/2)/(-1/2)| = 1
tan∅ = tanπ/4
∅ = π/4

∅ lies on 2nd quadrant so,
arg(z) = π - ∅
= π - π/4
= 3π/4

@jannatk0218