Find the multiplicative inverse of 7 + 24i.

Question 18 of 19

7 + 24i

Yanam BieapBIEAP Intermediate Board 2022Subjective· 2mImportance★★★★★

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The inverse of $7+24i$ is $\dfrac{7}{625}-\dfrac{24}{625}i$ .

The multiplicative inverse of a non-zero complex number $z$ is $z^{-1}=\dfrac{1}{z}=\dfrac{\bar z}{z\bar z}=\dfrac{\bar z}{|z|^2}$ .

Here $z = 7+24i$ , so $\bar z = 7-24i$ and $|z|^2 = 7^2+24^2 = 49+576 = 625$ .

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Q.Find the multiplicative inverse of $7 + 24i$ .