Question

If ${(x+iy)}^{1/3}=2+3i,$ then $3x+2y$ is equal to

• A. $-20$
• B. $-60$
• C. $-120$
• D. $60$
• E. $156$

Answer 1

Answer: (C)

Given, ${(x+iy)}^{1/3}=2+3i$
$\Rightarrow$ $x+iy={(2+3i)}^3$
$\Rightarrow$ $x+iy=-46+9i$
$\Rightarrow$ $x=-46,y=9$
$\therefore$ $3x+2y=3\times (-46)+2\times 9$
$=-138+18=-120$