Question:
$\left(\frac{1}{1-2i} + \frac{3}{1+i}\right) \left(\frac{3+4i}{2-4i}\right)$ is equal to :
$\left(\frac{1}{1-2i} + \frac{3}{1+i}\right) \left(\frac{3+4i}{2-4i}\right)$ is equal to :
Updated On: Jul 2, 2022
- $\frac{1}{2}+\frac{9}{2}i$
- $\frac{1}{2}-\frac{9}{2}i$
- $\frac{1}{4}-\frac{9}{4}i$
- $\frac{1}{4}+\frac{9}{4}i$
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Let $z = \left(\frac{1}{1-2i} + \frac{2}{1+i}\right) \left(\frac{3+4i}{2-4i}\right) $
$= \left[\frac{1+i+3-6i}{\left(1-2i\right)\left(1+i\right)}\right] \left[\frac{3+4i}{2-4i}\right]$
$= \left[\frac{4-5i}{3-i}\right]\left[\frac{3+4i}{2-4i}\right] = \left[\frac{32+i}{2-14i}\right]$
$= \frac{32+i}{2-14i}\times\frac{2+14i}{2+14i} = \frac{64+448i+2i-14}{4+196}$
$= \frac{50+450i}{200} = \frac{1}{4} + \frac{9}{4}i$
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 \( z = x + iy \) satisfies the equation \[ z^2 + az + a^2 = 0, \quad a \in \mathbb{R}, \] then:
- 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.
