# Find the Multiplicative Inverse of the Following Complex Number: 4 − 3i - Mathematics

Find the multiplicative inverse of the following complex number:

4 − 3i

#### Solution

$z = 4 - 3i$

$\text { Then,} \frac{1}{z} = \frac{1}{4 - 3i} \times \frac{4 + 3i}{4 + 3i}$

$= \frac{4 + 3i}{16 - 9 i^2}$

$= \frac{4 + 3i}{25}$

$= \frac{4}{25} + \frac{3}{25}i$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 13 Complex Numbers
Exercise 13.2 | Q 4.3 | Page 32