If z = x + iy is a complex number satisfying | vedclass

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

Question

(D) Given the equation $\left| z + \frac{i}{2} \right|^2 = \left| z - \frac{i}{2} \right|^2$. Substitute $z = x + iy$: $\left| x + iy + \frac{i}{2} \r

Vedclass · Accepted Answer

$x$-axis

Vedclass · Answer

(D) Given the equation $\left| z + \frac{i}{2} \right|^2 = \left| z - \frac{i}{2} \right|^2$. Substitute $z = x + iy$: $\left| x + iy + \frac{i}{2} \right|^2 = \left| x + iy - \frac{i}{2} \right|^2$ $\left| x + i(y + \frac{1}{2}) \right|^2 = \left| x + i(y - \frac{1}{2}) \right|^2$ Using the property $|a + ib|^2 = a^2 + b^2$: $x^2 + (y + \frac{1}{2})^2 = x^2 + (y - \frac{1}{2})^2$ $x^2 + y^2 + y + \frac{1}{4} = x^2 + y^2 - y + \frac{1}{4}$ $y = -y$ $2y = 0$ $y = 0$ This represents the $x$-axis.

If $z = x + iy$ is a complex number satisfying $\left| z + \frac{i}{2} \right|^2 = \left| z - \frac{i}{2} \right|^2$,then the locus of $z$ is

Similar Questions

Among the following compounds,which one is not responsible for the depletion of the ozone layer?

Which one of the following statements is not correct?

Cannizzaro reaction is not shown by

The angle between the asymptotes of the hyperbola $x^2-3y^2=3$ is

Animals devoid of respiratory,excretory,and circulatory organs are:

Vedclass Test Series

Exam Paper Generator

Online Exam Module