If ∣∣z2z1∣∣=1 and arg(z1z2)=0, then

Since we know that,(z1)(z2)=∣z1∣∣z2∣eiarg(z1z2)=∣z2∣2ei(0),(becausearg(z1z2)=0and∣z1∣=∣z2∣)⇒(z1)(z2)=∣z2∣2The other options are not true.

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If | {z_1}{z_2} | = 1 and arg(z_1z_2)=0, then

Question

If $∣ ∣ \frac{z _{1}}{z _{2}} ∣ ∣ = 1$ and $a r g (z_{1} z_{2}) = 0$ , then

z_{1} = z_{2}

∣ z_{2} ∣^{2} = z_{1} z_{2}

z_{1} z_{2} = 1

none of these

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Elijah Discussed

∣ ∣ \frac{z _{1}}{z _{2}} ∣ ∣ = 1

and

a r g (z_{1} z_{2}) = 0

, then

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Text solutionVerified

Since we know that,
$(z_{1}) (z_{2}) = ∣ z_{1} ∣∣ z_{2} ∣ e^{ia r g (z_{1} z_{2})} = ∣ z_{2} ∣^{2} e^{i (0)}, (b ec a u se a r g (z_{1} z_{2}) = 0 an d ∣ z_{1} ∣ = ∣ z_{2} ∣) \Rightarrow (z_{1}) (z_{2}) = ∣ z_{2} ∣^{2}$
The other options are not true.