Question

If $\frac{(1+i{)}^3}{(1-i{)}^3}-\frac{(1-i{)}^3}{(1+i{)}^3}=x+iy$

• A. $x=0,y=-2$
• B. $x=-2,y=0$
• C. $x=1,y=1$
• D. $x=-1,y=1$

Answer 1

Answer: (A)

$\frac{(1+i{)}^3}{(1-i{)}^3}-\frac{(1-i{)}^3}{(1+i{)}^3}=x+iy$
$\Rightarrow \frac{{\left(1+i^2+2i\right)}^3-{\left(1+i^2-2i\right)}^3}{{\left(1-i^2\right)}^3}=x+iy$
$\Rightarrow \frac{8i^3+8i^3}{2^3}=x+iy$
$\Rightarrow 2i^3=x+iy$
$\Rightarrow -2i=x+iy$
$\Rightarrow x=0,y=-2$