Question

What is the product of the complex number z1 and it’s conjugate? PLEASE HELP GRAPH in picture

Answer 1

Answer:

The product is 25

Step-by-step explanation:

we know that

The complex number z1 is equal to

z1=(-4-3i)

we know that

To find the complex conjugate of (-4 - 3i) we change the sign of the imaginary part

so

The conjugate is equal to (-4+3i)

therefore

$(-4-3i)(-4+3i)=16-9(-1)=25$

Answer 2

Answer:

$(-4-3i) (- 4 + 3i) = 25$

Step-by-step explanation:

Notice in the graph that z1 has a real component of -4 and an imaginary component of -3.

Then we know that:

$z_1 = -4-3i$

By definition for an imaginary number of the form $a-bi$ its conjugate will always be the number $a + bi$

So the conjugate of $z_1$ is:

$-4 + 3i$

The product of both numbers is:

$(-4-3i) (- 4 + 3i) = 16-12i + 12i-9i ^ 2\\\\(-4-3i) (- 4 + 3i) = 16-9 (-1)\\\\(-4-3i) (- 4 + 3i) = 16 + 9\\\\(-4-3i) (- 4 + 3i) = 25$