Question

simplify and express (1+i)^3-(1-i)^3

Answer 1

Given,

( 1 + i )³ - ( 1 - i )³

{a³-b³ =(a-b) (a²+ab+b²) }

.°. [ { ( 1 + i ) - ( 1 - i ) } { ( 1 + i )² + ( 1 + i ) ( 1 - i ) + ( 1 - i )² } ]

.°. [ ( 1 + i - 1 + i ) { ( 1² + 2*1*i + i² ) + ( 1² - i² ) + ( 1² - 2*1*i + i² )} ]

[ 2i {( 1 + 2i + i² ) + (1 - i² ) + ( 1 - 2i + i² )} ]

[ 2i ( 1 + 2i + i² + 1 - i² + 1 - 2i + i² ) ]

[ 2i ( 3 + i² ) ]

.°. 6i + 2i³