Question:
If $\arg(z_1) = \arg(z_2)$, then
If $\arg(z_1) = \arg(z_2)$, then
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Same argument means same direction → scalar multiple relation.
Updated On: Apr 30, 2026
- $z_2 = kz_1^{-1}, (k>0)$
- $z_2 = kz_1, (k>0)$
- $|z_2| = |z_1|$
- $z_1 = z_2$
- $|z_2| = |z_1|$
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The Correct Option is B
Solution and Explanation
Concept:
Two complex numbers having same argument lie on same ray from origin.
Step 1: Write polar forms. \[ z_1 = r_1(\cos\theta + i\sin\theta) \] \[ z_2 = r_2(\cos\theta + i\sin\theta) \]
Step 2: Relate them. \[ z_2 = \frac{r_2}{r_1} z_1 \] Let: \[ k = \frac{r_2}{r_1} > 0 \] \[ z_2 = kz_1 \] \[ \boxed{z_2 = kz_1, \; k>0} \]
Step 1: Write polar forms. \[ z_1 = r_1(\cos\theta + i\sin\theta) \] \[ z_2 = r_2(\cos\theta + i\sin\theta) \]
Step 2: Relate them. \[ z_2 = \frac{r_2}{r_1} z_1 \] Let: \[ k = \frac{r_2}{r_1} > 0 \] \[ z_2 = kz_1 \] \[ \boxed{z_2 = kz_1, \; k>0} \]
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