Question:
If z =$\frac{2-i}{i}$ = , then Re(z$^2$) + lm(z$^2$) is equal to
If z =$\frac{2-i}{i}$ = , then Re(z$^2$) + lm(z$^2$) is equal to
Updated On: Apr 8, 2024
- 1
- -1
- 2
- -2
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
$ z=\frac{2-i}{i} \Rightarrow z^{2}= \frac{(2-i)^{2}}{i^{2}} $
$=\frac{4-4 i-1}{-1}=\frac{3-4 i}{-1}=4 i-3$
Now, $ \operatorname{Re}\left(z^{2}\right) =-3$ and $ \operatorname{lm}\left(z^{2}\right)=4$
$\therefore \operatorname{Re}\left(z^{2}\right)+\operatorname{lm}\left(z^{2}\right) =-3+4=1$
$=\frac{4-4 i-1}{-1}=\frac{3-4 i}{-1}=4 i-3$
Now, $ \operatorname{Re}\left(z^{2}\right) =-3$ and $ \operatorname{lm}\left(z^{2}\right)=4$
$\therefore \operatorname{Re}\left(z^{2}\right)+\operatorname{lm}\left(z^{2}\right) =-3+4=1$
Was this answer helpful?
0
0
Top Questions on 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
Let α,β be the roots of the equation, ax2+bx+c=0.a,b,c are real and sn=αn+βn and \(\begin{vmatrix}3 &1+s_1 &1+s_2\\1+s_1&1+s_2 &1+s_3\\1+s_2&1+s_3 &1+s_4\end{vmatrix}=\frac{k(a+b+c)^2}{a^4}\) then k=
- WBJEE - 2023
- Mathematics
- Complex Numbers and Quadratic Equations
- For $z \in C$ if the minimum value of $(| z -3 \sqrt{2}|+| z - p \sqrt{2} i |)$ is $5 \sqrt{2}$, then a value of $p$ is ______
- JEE Main - 2023
- Mathematics
- Complex Numbers and Quadratic Equations
- The remainder when $(11)^{1011}+(1011)^{11}$ is divided by $9$ is
- JEE Main - 2023
- Mathematics
- Complex Numbers and Quadratic Equations
- If the shortest between the lines $\frac{x+\sqrt{6}}{2}=\frac{y-\sqrt{6}}{3}=\frac{z-\sqrt{6}}{4}$ and $\frac{x-\lambda}{3}=\frac{y-2 \sqrt{6}}{4}=\frac{z+2 \sqrt{6}}{5}$ is $6$ , then the square of sum of all possible values of $\lambda$ is
- JEE Main - 2023
- Mathematics
- Complex Numbers and Quadratic Equations
View More Questions
Questions Asked in KEAM exam
- A Spherical ball is subjected to a pressure of 100 atmosphere. If the bulk modulus of the ball is 1011 N/m2,then change in the volume is:
- KEAM - 2023
- mechanical properties of solids
- Two identical solid spheres,each of radius 10cm,are kept in contact. If the mass of inertia of this system about the tangent passing through the point of contact is 0. Then mass of each sphere is:
- KEAM - 2023
- System of Particles & Rotational Motion
- The value of a(≠0) for which the equation \(\frac{1}{2}(x-2)^2+1=\sin(\frac{a}{x})\) holds is/are
- KEAM - 2023
- Trigonometric Functions
- \(∫xlog(1+x^2)dx=\)?
- KEAM - 2023
- Integration by Parts
- A uniform thin rod of mass 3kg has a length of 1m. If a point mass of 1kg is attached to it at a distance of 40cm from its center,the center of mass shifts by a distance of:
- KEAM - 2023
- System of Particles & Rotational Motion
View More Questions
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.
