Question

Convert (8, 2π/3) into Argand plane representation.

(a) (-4, 4\(\sqrt{3}\))

(b) (4, 4\(\sqrt{3}\))

(c) (4\(\sqrt{3}\), 4)

(d) (-4\(\sqrt{3}\), 4)

The question was asked during a job interview.

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

Answer 1

Right option is (a) (-4, 4\(\sqrt{3}\))

To explain I would say: To convert polar representation (r, θ) into argand plane (x, y), substitute x=r cos θ and y=r sin θ.

x=8cos 2π/3 = 8cos(π-π/3) = 8(-1/2) = -4.

y=8sin 2π/3 = 8sin(π-π/3) = 8(\(\sqrt{3}\)/2) = 4\(\sqrt{3}\).