What is the **multiplicative inverse** of $z = 4 + 3i$ in $a + ib$ form?
A$\dfrac{4}{25} + \dfrac{3}{25}i$
B$\dfrac{4}{7} - \dfrac{3}{7}i$
C$\dfrac{4}{25} - \dfrac{3}{25}i$
D$4 - 3i$
Answer & Solution
Correct answer: C. $\dfrac{4}{25} - \dfrac{3}{25}i$
$\dfrac{1}{z} = \dfrac{\bar{z}}{|z|^{2}} = \dfrac{4 - 3i}{25}$.
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