what is quotient of the complex number 4-3i divided by its conjugate?

1 answer

To find the quotient of a complex number divided by its conjugate, we need to multiply both the numerator and denominator by the conjugate of the denominator.

The complex number in this case is 4-3i, and its conjugate is 4+3i.

So, when we multiply the numerator and denominator by the conjugate of the denominator, we get:

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

Expanding both the numerator and denominator:

Numerator:
= (4*4) + (4*3i) - (3i*4) - (3i*3i)
= 16 + 12i - 12i - 9
= 7

Denominator:
= (4*4) + (4*3i) - (3i*4) - (3i*3i)
= 16 + 12i - 12i - 9
= 7

Therefore, the quotient of the complex number 4-3i divided by its conjugate is 7.