SATHEE: Complex Numbers 3 Question 5

Complex Numbers 3 Question 5

5. Let $z$ and $w$ be two non-zero complex numbers such that $| z | = | w |$ and $\arg (z) + \arg (w) = π$ , then $z$ equals

(1995, 2M)

(a) $w$

(b) $- w$

(d) $- \bar{w}$

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Answer:

Correct Answer: 5. (d)

Solution:

Since, $| z | = | w |$ and $\arg (z) = π - \arg (w)$

$\begin{array}{ll} Let & w = r e^{i θ}, then \bar{w} = r e^{- i θ} \\ ∴ & z = r e^{i (π - θ)} = r e^{i π} \cdot e^{- i θ} = - r e^{- i θ} = - \bar{w} \end{array}$

Complex Numbers 3 Question 5

5. Let $z$ and $w$ be two non-zero complex numbers such that $| z | = | w |$ and $\arg (z) + \arg (w) = π$ , then $z$ equals

Answer:

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Complex Numbers 3 Question 5

5. Let z and w be two non-zero complex numbers such that |z|=|w| and arg⁡(z)+arg⁡(w)=π, then z equals

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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5. Let $z$ and $w$ be two non-zero complex numbers such that $| z | = | w |$ and $\arg (z) + \arg (w) = π$ , then $z$ equals