First slide

Algebra of complex numbers

Question

Let $z_{1}, z_{2}$ be two complex numbers such that $z_{1} \neq 0$ and $z_{2} / z_{1}$ 1 is purely real, then $|\frac{2 i z_{1} + 5 z_{2}}{2 i z_{1} - 5 z_{2}}|$ is equal to

Moderate

A

3
B

2
C

1
D

0

Solution

Suppose $z_{2} / z_{1} = a,$ where $a \in R$
Now, , $|\frac{2 i z_{1} + 5 z_{2}}{2 i z_{1} - 5 z_{2}}| = |\frac{2 i + 5 (z_{2} / z_{1})}{2 i - 5 (z_{2} / z_{1})}| = |\frac{2 i + 5 a}{2 i - 5 a}| = 1$

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