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Complex Numbers — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSComplex Numbers3 Marks
Question
Find the multiplicative inverse of the following complex numbers: $4-3\text{i}$
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Answer

Let $\text{z}=4-3\text{i}$ $\text{z}^{-1}=\frac{4}{4^2+(-3)^2}-\frac{(-3)}{4^2+(-3)^2}$ $=\frac{4}{16+9}+\frac{3}{16+9}\text{i}$ $=\frac{4}{25}+\frac{3}{25}\text{i}$

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