Question:
If $\frac {2z_1} {3z_2} $ is a purely imaginary number, then $|\frac {z_1-z_2} {z_1+z_2}|$ is equal to
If $\frac {2z_1} {3z_2} $ is a purely imaginary number, then $|\frac {z_1-z_2} {z_1+z_2}|$ is equal to
Updated On: Jul 6, 2022
- $\frac {3} {2}$
- 1
- $\frac {2} {3}$
- $\frac {4} {9}$
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Let $\frac{2z_{1}}{3z_{2}}=id$
$\therefore \left|\frac{z_{1}-z_{2}}{z_{1}+z_{2}}\right|=\left|\frac{\frac{z_{1}}{z_{2}}-1}{\frac{z_{1}}{z_{2}}-1}\right|$
$=\left|\frac{\frac{3ki}{2}-1}{\frac{3ki}{2}+1}\right|$
$=\left|\frac{3ki-2}{3ki+2}\right|=1$
Was this answer helpful?
0
0
Top Questions on Complex Numbers and Quadratic Equations
- If \(z = 1 - \sqrt{3}\,i\), then \(z^3 - 3z^2 + 3z = \;?\)
- TS EAMCET - 2024
- Mathematics
- Complex Numbers and Quadratic Equations
- The minimum value of \(| z+ \frac{3+4i}{2}|, |z| \leq 1\) is,
- JEE Main - 2024
- Mathematics
- Complex Numbers and Quadratic Equations
- If \( Z_1, Z_2, Z_3 \) are three complex numbers with unit modulus such that \[ |Z_1 - Z_2|^2 + |Z_1 - Z_3|^2 = 4 \] then \[ Z_1 Z_2 + \overline{Z_1} Z_2 + Z_1 Z_3 + \overline{Z_1} Z_3 = \]
- TS EAMCET - 2024
- Mathematics
- Complex Numbers and Quadratic Equations
- If \( Z_1 = \sqrt{3} + i\sqrt{3} \) and \( Z_2 = \sqrt{3} + i \), and \[ \left( \frac{Z_1}{Z_2} \right)^{50} = x + iy, \] then the point \( (x,y) \) lies in:
- TS EAMCET - 2024
- Mathematics
- Complex Numbers and Quadratic Equations
- If \( \omega \) is the complex cube root of unity and \[ \left( \frac{a + b\omega + c\omega^2}{c + a\omega + b\omega^2} \right)^k + \left( \frac{a + b\omega + c\omega^2}{b + a\omega^2 + c\omega} \right)^2 = 2, \] then \( 2k + 1 \) is always:
- TS EAMCET - 2024
- Mathematics
- Complex Numbers and Quadratic Equations
View More Questions
Notes on Complex Numbers and Quadratic Equations
- Complex Numbers and Quadratic Equations Mathematics
- NCERT Solutions for class 11 mathematics Chapter 5 Complex Numbers and Quadratic Equations
- Complex Numbers Quadratic Equations Important Questions Mathematics
- NCERT Solutions for Class 11 Maths Chapter 5 Exercise 5 1
- NCERT Solutions for Class 11 Maths Chapter 5 Exercise 5 2
- NCERT Solutions for Class 11 Maths Chapter 5 Exercise 5 3
Concepts Used:
Complex Numbers and Quadratic Equations
Complex Number: Any number that is formed as a+ib is called a complex number. For example: 9+3i,7+8i are complex numbers. Here i = -1. With this we can say that i² = 1. So, for every equation which does not have a real solution we can use i = -1.
Quadratic equation: A polynomial that has two roots or is of the degree 2 is called a quadratic equation. The general form of a quadratic equation is y=ax²+bx+c. Here a≠0, b and c are the real numbers.
