If z = x + iy and z^2 = (i bar{z})^2,then | vedclass

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

Question

(B) Given $z = x + iy$,then $\bar{z} = x - iy$.Given the equation $z^2 = (i \bar{z})^2$.Expanding both sides: $z^2 = i^2 (\bar{z})^2$.Since $i^2 = -1$

Vedclass · Accepted Answer

$y = \pm x$

Vedclass · Answer

(B) Given $z = x + iy$,then $\bar{z} = x - iy$.Given the equation $z^2 = (i \bar{z})^2$.Expanding both sides: $z^2 = i^2 (\bar{z})^2$.Since $i^2 = -1$,we have $z^2 = -(\bar{z})^2$,which implies $z^2 + (\bar{z})^2 = 0$.Substitute $z = x + iy$ and $\bar{z} = x - iy$:$(x + iy)^2 + (x - iy)^2 = 0$.$(x^2 - y^2 + 2ixy) + (x^2 - y^2 - 2ixy) = 0$.$2(x^2 - y^2) = 0$.$x^2 - y^2 = 0$.$x^2 = y^2$,which means $y = \pm x$.

If $z = x + iy$ and $z^2 = (i \bar{z})^2$,then

Similar Questions

The points in the Argand plane represented by the complex conjugates of $1+2i, 2-3i, 3-4i$:

If $P$ is a complex number whose modulus is $1$,then the equation $\left(\frac{1+iz}{1-iz}\right)^4=P$ has

$A$ point $z$ moves on the Argand diagram in such a way that $|z - 3i| = 2$. Then its locus will be:

Which of the following equations can represent a triangle in the complex plane?

Let the complex numbers $z_1, z_2$ and $z_3$ be the vertices of an equilateral triangle. Let $z_0$ be the circumcentre of the triangle,then $z_1^2 + z_2^2 + z_3^2 = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module