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Question: Modulus of \(\left| \frac{z_{1} + z_{2}}{z_{1} - z_{2}} \right|\)is....

Modulus of ∣z1+z2z1−z2∣\left| \frac{z_{1} + z_{2}}{z_{1} - z_{2}} \right|is.

A

1

B

½

C

2

D

z1z2\frac{z_{1}}{z_{2}}

Answer

1

Explanation

Solution

=[r12+r22+2r1r2cos⁡(θ1−θ2)]1/2=[(r1+r2)2]1/2arg(z2)=θ= \lbrack r_{1}^{2} + r_{2}^{2} + 2r_{1}r_{2}\cos(\theta_{1} - \theta_{2})\rbrack^{1/2} = \lbrack(r_{1} + r_{2})^{2}\rbrack^{1/2}arg(z_{2}) = \theta

Modulus =cos⁡(θ1−θ2)=1⇒θ1−θ2=0⇒θ1=θ2\cos(\theta_{1} - \theta_{2}) = 1 \Rightarrow \theta_{1} - \theta_{2} = 0 \Rightarrow \theta_{1} = \theta_{2}.