Question

Find the polar form of the complex number
1+2i/1-3i​

Answer 1

Step-by-step explanation:

We are given, Z = (1 + 2i)/(1 – 3i). As x < 0 and y > 0, Z lies in 2nd quadrant and the value of θ is π/2 ≤ θ ≤ π. Therefore, the polar form of (1 + 2i)/(1 – 3i) is 1/√2 (cos (3π/4) + i sin (3π/4))

Answer 2

$\huge{\textbf{\textsf{\pink{Answer\::}}}}$

∴ arg(z) = θ = (π - α) = (π - π4) = 3π4

Thus, r=|z|=1√2andθ=3π4.

Hence, the required polar form is,

→ z = 1√2(cos3π4+i sin3π4).