Question

If 3^49 (x+iy) = (3/2+i?3/2)^100, y belongs to , x = ky then k=?

Answer 1

Answer:

- 1/√3

Step-by-step explanation:

Given If 3^49 (x+iy) = (3/2+i?3/2)^100, y belongs to , x = ky then k=?

We are given

3^49 (x + i y) = (3/2 + √3/2 i)^100

3^49(x + i y) = 3^50 (i / 2, √3/2)^100

 x + iy = 3(cos 180/6 + i sin 180/6)^100

We know that (cosФ + isinФ)^x = cosxФ + isinxФ

  So x + iy =3( cos 50π / 6 + isin 50π/3)

  = 3 (cos 17 π - π/3) + i sin(17π - π/3)

  = 3 (- cosπ/3 + i sinπ/3)

= 3(- 1/2 + i √3/2)

So x = - 3/2, y = 3√3/2

 x = ky given

So k = x/y

= - 3/ 2 / 3√3/2

k = - 1/√3