Question

Convert -1+i into polar form.

(a) \(\sqrt{2}\), 5π/4

(b) \(\sqrt{2}\), 3π/4

(c) –\(\sqrt{2}\), π/4

(d) \(\sqrt{2}\), π/4

The question was posed to me in an interview.

Enquiry is from Argand Plane and Polar Representation in division Complex Numbers and Quadratic Equations of Mathematics – Class 11

Answer 1

Right choice is (b) \(\sqrt{2}\), 3π/4

To elaborate: 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 So, θ is in 2^nd quadrant since sin is positive and cos is negative.

tan θ = -1 => tan θ = -tan π/4

=> tan θ = tan (π-π/4) = tan 3π/4

=> θ=3π/4.