Question

Evaluate : ${\left(1+i\right)}^6+{\left(1-i\right)}^3$.

• A. $-2-10i$
• B. $2-10i$
• C. $-2+10i$
• D. $2+10i$

Answer 1

Answer: (A)

${\left(1+i\right)}^6={\left\{{\left(1+i\right)}^2\right\}}^3$
$={\left(2i\right)}^3=8i^3=-8i$
and ${\left(1-i\right)}^3=1-i^3-3i+3i^2$
$=1+i-3i-3$
$=-2-2i$
$\therefore {\left(1+i\right)}^6+{\left(1-i\right)}^3$
$=-8i-2-2i$
$=-2-10i$