SATHEE: Complex Numbers 2 Question 15

Complex Numbers 2 Question 15

15.

If $z_{1}, z_{2}$ and $z_{3}$ are complex numbers such that $| z_{1} | = | z_{2} | = | z_{3} | = | \frac{1}{z_{1}} + \frac{1}{z_{2}} + \frac{1}{z_{3}} | = 1$ , then $| z_{1} + z_{2} + z_{3} |$ is

(a) equal to 1

(b) less than 1

(d) equal to 3

$(2000, 2 M)$

Show Answer

Answer:

Correct Answer: 15. (a)

Solution:

Given,

$| z_{1} | = | z_{2} | = | z_{3} | = 1$

Now, $| z_{1} | = 1$

$\Rightarrow$ ${| z_{1} |}^{2} = 1 \Rightarrow z_{1} {\bar{z}}_{1} = 1$

Similarly, $z_{2} {\bar{z}}_{2} = 1, z_{3} {\bar{z}}_{3} = 1$

Again now, $\frac{1}{z_{1}} + \frac{1}{z_{2}} + \frac{1}{z_{3}} = 1$

$\Rightarrow | {\bar{z}}_{1} + {\bar{z}}_{2} + {\bar{z}}_{3} | = 1 \Rightarrow \overset{―}{| z_{1} + z_{2} + z_{3} |} = 1$

$\Rightarrow | z_{1} + z_{2} + z_{3} | = 1$

Complex Numbers 2 Question 15

15.

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Complex Numbers 2 Question 15

15.

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Menu