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Properties of Modulus

If 5 z 1/7 z ...

Question

If $\frac{5 z_{1}}{7 z_{2}}$ is purely imaginary then the value of $∣ ∣ ∣ \frac{2 z_{1} + 3 z_{2}}{2 z_{1} - 3 z_{2}} ∣ ∣ ∣$ is

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Solution

Let $\frac{z_{1}}{z_{2}} = i b, b \in R$
Now , $∣ ∣ ∣ \frac{2 z_{1} + 3 z_{2}}{2 z_{1} - 3 z_{2}} ∣ ∣ ∣ = ∣ ∣ ∣ ∣ ∣ \frac{2 \frac{z_{1}}{z_{2}} + 3}{2 \frac{z_{1}}{z_{2}} - 3} ∣ ∣ ∣ ∣ ∣$
$= ∣ ∣ ∣ \frac{2 i b + 3}{2 i b - 3} ∣ ∣ ∣$
$= \frac{| 2 b i + 3 |}{| 2 b i - 3 |} = 1$ $[∵ ∣ ∣ ∣ \frac{z_{1}}{z_{2}} ∣ ∣ ∣ = \frac{| z_{1} |}{| z_{2} |}]$

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Similar questions

\frac{5 z_{1}}{7 z_{2}}

is purely imaginary, then

∣ ∣ ∣ \frac{2 z_{1} + 3 z_{2}}{2 z_{1} - 3 z_{2}} ∣ ∣ ∣ i s

\frac{5 z_{2}}{7 z_{1}}

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∣ ∣ ∣ \frac{2 z_{1} + 3 z_{2}}{2 z_{1} - 3 z_{2}} ∣ ∣ ∣

Q. Assertion :If

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Properties of Modulus

Standard XII Mathematics

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