SATHEE: Complex Numbers 2 Question 19

Complex Numbers 2 Question 19

19.

If $z = x + i y$ and $w = (1 - i z) / (z - i)$ , then $| w | = 1$ implies that, in the complex plane

(1983, 1M)

(a) $z$ lies on the imaginary axis

(b) $z$ lies on the real axis

(d) None of these

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Answer:

Correct Answer: 19. (b)

Solution:

Since, $| w | = 1 \Rightarrow \frac{1 - i z}{z - i} = 1$

$\begin{array}{lll} \Rightarrow & | z - i | = | 1 - i z | \\ \Rightarrow & | z - i | = | z + i | [∵ | 1 - i z | = | - i | | z + i | = | z + i |] \end{array}$

$∴$ It is a perpendicular bisector of $(0, 1)$ and $(0, - 1)$ i.e. $X$ -axis. Thus, $z$ lies on the real axis.

Complex Numbers 2 Question 19

19.

Answer:

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Complex Numbers 2 Question 19

19.

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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