The figure in the complex plane given by 10 z | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let $z = x + iy$,then $\bar{z} = x - iy$.We have $z \bar{z} = x^2 + y^2$,$z^2 = x^2 - y^2 + 2ixy$,and $\bar{z}^2 = x^2 - y^2 - 2ixy$.Substituting

Vedclass · Accepted Answer

a straight line

Vedclass · Answer

(A) Let $z = x + iy$,then $\bar{z} = x - iy$.We have $z \bar{z} = x^2 + y^2$,$z^2 = x^2 - y^2 + 2ixy$,and $\bar{z}^2 = x^2 - y^2 - 2ixy$.Substituting these into the equation $10 z \bar{z} - 3(z^2 + \bar{z}^2) + 4i(z^2 - \bar{z}^2) = 0$:$10(x^2 + y^2) - 3(2(x^2 - y^2)) + 4i(4ixy) = 0$$10(x^2 + y^2) - 6(x^2 - y^2) - 16xy = 0$$10x^2 + 10y^2 - 6x^2 + 6y^2 - 16xy = 0$$4x^2 - 16xy + 16y^2 = 0$Dividing by $4$,we get $x^2 - 4xy + 4y^2 = 0$,which is $(x - 2y)^2 = 0$.This represents the straight line $x - 2y = 0$.

The figure in the complex plane given by $10 z \bar{z} - 3(z^2 + \bar{z}^2) + 4i(z^2 - \bar{z}^2) = 0$ is

Similar Questions

The region of the Argand plane defined by $|z - 1| + |z + 1| \le 4$ is

Let $O$ be the origin and $A$ be the point $z_{1} = 1 + 2i$. If $B$ is the point $z_{2}$ with $\operatorname{Re}(z_{2}) < 0$, such that $\triangle OAB$ is a right-angled isosceles triangle with $OB$ as the hypotenuse, then which of the following is $NOT$ true?

If $z=x+iy$,then the equation $|z+1|=|z-1|$ represents

For all complex numbers $z_1, z_2$ satisfying $|z_1| = 12$ and $|z_2 - 3 - 4i| = 5$,the minimum value of $|z_1 - z_2|$ is

If the imaginary part of $\frac{2 z+1}{i z+1}$ is $-2$,then the locus of the point representing $z$ in the complex plane is

Vedclass Test Series

Exam Paper Generator

Online Exam Module