Let and be complex numbers such that is purely imaginary. What is equal to? मान लीजिए Z ₁ और इस प्रकार की सम्मिश्र संख्याएं हैं कि शुद्धतः अधिकल्पित संख्या किसके बराबर है ?

Explanation: To solve this, we use the property that a complex number is purely imaginary if and only if . Given Condition: Let . Since is purely imaginary, we have: Dividing by : Evaluating the Required Expression: Let . Squaring both sides: Expanding the numerator and denominator: Substitution: We know that and . Also, from our condition, . Therefore, . Correct Option: (d) 1

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NDA 2026 — Mathematics PYQ

NDA | Mathematics | 2026

Let $Z_{1}$ and $Z_{2}$ be complex numbers such that $\frac{3 Z _{1}}{4 Z _{2}}$ is purely imaginary. What is $\frac{Z _{1} + Z _{2}}{Z _{1} - Z _{2}}$ equal to?

मान लीजिए Z₁ और $Z_{2}$ इस प्रकार की सम्मिश्र संख्याएं हैं कि $\frac{3 Z _{1}}{4 Z _{2}}$ शुद्धतः अधिकल्पित संख्या $\frac{Z _{1} + Z _{2}}{Z _{1} - Z _{2}}$ किसके बराबर है ?

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