Question

Find the multiplicative inverse of $2-3i$.

• A. $2/13+i(3/13)$
• B. $2/13-i(3/13)$
• C. $2+3i$
• D. None of these

Answer 1

Answer: (A)

Let $z=2-3i$ , then, $z^{-1}=\frac{1}{2-3i}$
$=\frac{2+3i}{\left(2-3i\right)\left(2+3i\right)}$
$=\frac{2+3i}{2^2-{\left(3i\right)}^2}$
$=\frac{2+3i}{13}$
$=\frac{2}{13}+\frac{3}{13}i$