Question

Z1 = 3 + 2i and z2 = -5 -3i

What are the conjugates of z1 and z2 ?
What is the conjugate of the product of z1 and z2?

Answer 1

The conjugates of z1 = 3 + 2i and z2 = -5 - 3i are 3 - 2i and -5 + 3i, respectively. The conjugate of the product of z1 and z2 is -21 + 19i.

Step-by-step explanation:

The conjugate of a complex number is obtained by changing the sign of its imaginary part.

The conjugate of z1 = 3 + 2i is 3 - 2i, and the conjugate of z2 = -5 - 3i is -5 + 3i.

To find the conjugate of the product of z1 and z2, we multiply z1 and z2, and then take the conjugate of the result.

The product of z1 and z2 is (-5 - 3i)(3 + 2i) = -15 - 10i - 9i - 6i^2 = -21 - 19i, and the conjugate of -21 - 19i is -21 + 19i.

Answer 2

See below in bold.

Step-by-step explanation:

z1: 3 + 2i

The conjugate is 3 - 2i.

z2: -5 - 3i The conjugate is -5 + 3i.

The product z1 * z2 = (3 + 2i)(-5 - 3i)

= -15 - 9i - 10i - 6i^2

= -15 - 19i - 6*-1

= -15 - 19i + 6

= -9 - 19 i.

So it's conjugate is -9 +19 i.