What is the quotient of the complex number four subtract three divided by it’s conjugate

Answer 1

To find the quotient of a complex number divided by its conjugate, we first need to find the conjugate of the complex number.

The conjugate of a complex number is found by changing the sign of the imaginary part. In this case, the complex number is 4 - 3i, so its conjugate is 4 + 3i.

Now, we can divide the complex number by its conjugate:

(4 - 3i) / (4 + 3i)

To divide complex numbers, we need to multiply both the numerator and denominator by the conjugate of the denominator:

[(4 - 3i) * (4 - 3i)] / [(4 + 3i) * (4 - 3i)]

Expanding:

(16 - 12i - 12i + 9i^2) / (16 - 9i^2)

Simplifying:

(16 - 24i - 9) / (16 + 9)

(7 - 24i) / 25

Therefore, the quotient of the complex number (4 - 3i) divided by its conjugate is:

(7 - 24i) / 25