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  • Find the multiplicative inverse of each of the complex numbers. (12) sqrt 5 + 3i

Find the multiplicative inverse of each of the complex numbers.

Q: 12        \sqrt{5}+3i

Answers (1)

best_answer

Let    z = \sqrt{5}+3i
Then,
\bar z = \sqrt{5}-3i
And 
|z|^2 = (\sqrt5)^2+(3)^2 = 5+9 =14
Now, the multiplicative inverse is given by
z^{-1}= \frac{\bar z}{|z|^2}= \frac{\sqrt5-3i}{14}= \frac{\sqrt5}{14}-i\frac{3}{14}

Therefore, the multiplicative inverse is   \frac{\sqrt5}{14}-i\frac{3}{14}

Posted by

Gautam harsolia

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