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Algebra of Complex Numbers

Express the f...

Question

Express the following in the form of $a + b i$ and the value of $a$ and $b$ : $(1 + i) (1 - i)^{- 1}$ ?

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Solution

$\frac{1 + i}{1 - i} = \frac{i (- i + 1)}{1 - i} = i$
$a + i b = i ⟹ a = 0$ & $b = 1$

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