Complex number

Question

4+3i/(1-I)^3

Answer 1

(4+3i)/(1-i)^3  = ?

(1-i)^3 = 1 - (i)^3 - 3(1)(i){ 1 - i }

  = 1 + i - 3i  - 3 = -2( 1 + i )

Now (4+3i)/(1-i)^3  = (4+3i)/[-2(1+i)]  = -{ 2(1+i) + (2+i) }/[2(1+i)]

= -1 -  (2+i)/[2(1+i)]  = -1 -   { (2+i) (1-i) } /[2(1+i) (1-i)]  = -1 -  { 2 -2i + i - (i)(i) } /[2(1- i^2) ]

= -1 -  { 3 -i }/[2(2) ] = -1 - 3/4 + 1/4(i)  = -1.75 + 0.25i