Question

Convert -1-i into polar form.

(a) \(\sqrt{2}\), 5π/4

(b) \(\sqrt{2}\), 3π/4

(c) \(\sqrt{2}\), -3π/4

(d) \(\sqrt{2}\), π/4

This question was posed to me in an online interview.

This interesting question is from Argand Plane and Polar Representation topic in division Complex Numbers and Quadratic Equations of Mathematics – Class 11

Answer 1

Right answer is (c) \(\sqrt{2}\), -3π/4

The best I can explain: r=\(\sqrt{x^2+y^2} = \sqrt{(-1)^2+1^2} = \sqrt{1+1} = \sqrt{2}\).

r cos θ = -1 and r sin θ = -1 => θ is in 3^rd quadrant since sin and cos both negative.

tan θ = 1 => θ= -3π/4.