Question

If $(3-5i{)}^3$ can be expressed in the form $a+ib$ ,then the ordered pair $(a,b)$ is

• A. $(-198,10)$
• B. $(-198,-10)$
• C. $(198,-10)$
• D. $(198,10)$

Answer 1

The correct option is B $(-198,-10)$

We know that $(z_1-z_2{)}^3=z_1^3-z_2^3-3z_1{z}_2(z_1-z_2).$
$\therefore (3-5i{)}^3=3^3-(5i{)}^3-3\times 3\times 5i(3-5i)$
$=27-125i^3-135i+225i^2$
$=27+125i-135i-225\because [i^3=-i,i^2=-1]$
$=-198-10i$.