SATHEE: Complex Numbers 2 Question 5

Complex Numbers 2 Question 5

5. Let $z$ be a complex number such that $| z | + z = 3 + i$ (where $i = \sqrt{- 1}$ ).

Then, $| z |$ is equal to

(2019 Main, 11 Jan II)

(a) $\frac{\sqrt{34}}{3}$

(b) $\frac{5}{3}$

(d) $\frac{5}{4}$

Show Answer

Answer:

Correct Answer: 5. (b)

Solution:

We have, $| z | + z = 3 + i$

$\begin{array}{ll} Let & z = x + i y \\ ∴ & \sqrt{x^{2} + y^{2}} + x + i y = 3 + i \\ \Rightarrow & (x + \sqrt{x^{2} + y^{2}}) + i y = 3 + i \\ \Rightarrow & x + \sqrt{x^{2} + y^{2}} = 3 and y = 1 \\ Now, & \sqrt{x^{2} + 1} = 3 - x \\ \Rightarrow & x^{2} + 1 = 9 - 6 x + x^{2} \\ \Rightarrow & 6 x = 8 \Rightarrow x = \frac{4}{3} \\ ∴ & z = \frac{4}{3} + i \\ \Rightarrow & | z | = \sqrt{\frac{16}{9} + 1} = \sqrt{\frac{25}{9}} \Rightarrow | z | = \frac{5}{3} \end{array}$

Complex Numbers 2 Question 5

5. Let $z$ be a complex number such that $| z | + z = 3 + i$ (where $i = \sqrt{- 1}$ ).

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 5

5. Let z be a complex number such that |z|+z=3+i (where i=−1 ).

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Menu

5. Let $z$ be a complex number such that $| z | + z = 3 + i$ (where $i = \sqrt{- 1}$ ).