If 5 z 1 3 i z 2 is purely real, then find 5 3 z 1 − 7 z 2 3 z 1 + 7 z 2 .

Let 5 z 1 3 i z 2 = K (real) z 1 z 2 = 3 i 5 K 5 3 − 7 z 1 z 2 3 + 7 z 1 z 2 = 5 3 − 3 i 35 K 3 + 7 3 i 35 K 5 35 K − 9 i 35 K + 9 i = 5

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MathematicsComplex NumberGeneral(Modulus,Argument,Conjugate)Medium2 minQB

MathematicsMediuminteger

If $\frac{3 i z _{2}}{5 z _{1}}$ is purely real, then find $5 \frac{3 z _{1} + 7 z _{2}}{3 z _{1} - 7 z _{2}}$ .

Answer:

Solution:

Let $\frac{3 i z _{2}}{5 z _{1}} = K$ (real)

$\frac{z _{2}}{z _{1}} = \frac{5 K}{3 i}$

$5 \frac{3 + 7 \frac{z _{2}}{z _{1}}}{3 - 7 \frac{z _{2}}{z _{1}}} = 5 \frac{3 + 7 \frac{35 K}{3 i}}{3 - \frac{35 K}{3 i}}$

$5 \frac{35 K + 9 i}{35 K - 9 i} = 5$

Stream:JEESubject:MathematicsTopic:Complex NumberSubtopic:General(Modulus,Argument,Conjugate)

⏱ 2mℹ️ Source: QB

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