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Find the multiplicative inverse of the complex numbers given t

Question

Find the multiplicative inverse of the complex numbers given the following:
$4 - 3 i$

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Find the multiplicative inverse of the complex numbers given the following:

4 - 3 i

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Text solutionVerified

Let multiplicative inverse of

4 - 3 i

x

\Rightarrow x = \frac{1}{4 - 3 i}

Rationalize the denominator

\Rightarrow x = \frac{1}{4 - 3 i} \times \frac{4 + 3 i}{4 + 3 i}

\Rightarrow x = \frac{4 + 3 i}{4 ^{2} - ( 3 i ) ^{2}}

\Rightarrow x = \frac{4 + 3 i}{16 - ( - 9 )} = \frac{4 + 3 i}{16 + 9}

\Rightarrow x = \frac{4 + 3 i}{25}

The multiplicative inverse of

4 - 3 i

\frac{4 + 3 i}{25}

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Question Text	Find the multiplicative inverse of the complex numbers given the following: $4 - 3 i$
Answer Type	Text solution:1
Upvotes	150