Question
Find the conjugates of the following complex numbers: $\frac{1}{1+\text{i}}$
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Answer
Let $\text{z}=\frac{1}{1+\text{i}}$ $=\frac{1}{1+\text{i}}\times\frac{(1-\text{i})}{1-\text{i}}$ $=\frac{1+\text{i}}{1^2+1^2}$ $=\frac{1-\text{i}}{2}$ $\therefore\bar{\text{z}}=\frac{1-\text{i}}{2}$ $=\frac{1}{2}+\frac{1}{2}\text{i}$
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