Find the conjugates of the following complex numbers: 1 3+5i - Vidyadip

Question

Find the conjugates of the following complex numbers: $\frac{1}{3+5\text{i}}$

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Answer

Let $\text{z}=\frac{1}{3+5\text{i}}$ $=\frac{1}{3+5\text{i}}\times\frac{(3+5\text{i})}{3+5\text{i}}$ (On rationalising the denominator) $=\frac{3+5\text{i}}{3^2+5^2}$ $\Rightarrow\text{z}=\frac{3-5\text{i}}{9+25}$ So $\bar{\text{z}}=\frac{3-5\text{i}}{34}$ $=\frac{3}{34}+\frac{5}{34}\text{i}$

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