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Continuity of a Function

Let z1 and ...

Question

Let $z_{1} a n d z_{2}$ be nth roots of unity which subtends right angle at the origin, then n must be of form:

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Solution

$a r g \frac{z_{1}}{z_{2}} = \frac{π}{2}$

$\frac{z_{1}}{z_{2}} = i$

${(\frac{z_{1}}{z_{2}})}^{n} = i^{n} = 1$

$n = 4 k$

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