Question

1+7i/(2-i)^2 convert the following into polar form.​

Answer 1

Answer:

let z= 1+7I / (2-i)² = 1+7I/4-4i+i² = 1+7I/3-4i =

1+7I/3-4i × 3+4i/3+4i = -1+i

r= ।z। = √-1²+1² = √2

let a be the acute angle given by tan a =। img/re।

tan a= ।-1/1। = 1। => a = π/4

-1,1 will lie in 2 quadrant

o = arg = π-a = π -π/4 = 3π/4

hence the polar form of z is

r(cos 0 +sino) = √2(cos 3π/4 +o sin 3π/4)