Question

Find the equation in Cartesian coordinates of the locus of z if. |z| = 10​

Answer 1

Answer:

The locus of the equation is a circle with the radius 10.

Step-by-step explanation:

In the question,

We have been provided that,

|z| = 10

Also,

We know that, z = x + iy

So,

$|x+iy| = 10$

As,

We know that,

$|a + ib|=\sqrt{a^{2}+b^{2}}$

So,

Using the same in the given equation as well we get,

$\sqrt{x^{2}+y^{2}}=10$

So, on squaring both the sides we get,

$x^{2}+y^{2}=10^{2}\\x^{2}+y^{2}=100$

We know that the equation of the circle is given by,

$x^{2} +y^{2}= r^{2}$

where, r is the radius of the circle with the center at (0, 0).

So,

On comparing we get that,

The locus of the equation is a circle with the radius 10.