First slide

Algebra of complex numbers

Question

If ${(\frac{1 + i}{1 - i})}^{n} = - 1, n \in N$ then least value of $n$ is

Moderate

A

1
B

2
C

3
D

4

Solution

Write $1 = - i^{2}$ in the numerator, to obtain
$\begin{aligned} \frac{1 + i}{1 - i} = \frac{- i^{2} + i}{1 - i} = \frac{i (1 - i)}{1 - i} = i \\ ∴ - 1 = (\frac{1 + i}{1 - i}) = i^{n} \end{aligned}$
The least value of $n$ is 2.

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