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 is 4-3i, and its conjugate is 4+3i.
Therefore, the fraction becomes:
(4-3i) / (4+3i)
Multiplying both the numerator and denominator by the conjugate of the denominator:
[(4-3i)(4-3i)] / [(4+3i)(4-3i)]
Expanding both the numerator and denominator:
(16 - 12i - 12i + 9i^2) / (16 - 12i + 12i - 9i^2)
Simplify:
(16 - 24i + 9i^2) / (16 - 9i^2)
Remember that i^2 = -1:
(16 - 24i - 9) / (16 + 9)
Combine like terms:
(7 - 24i) / 25
So, the quotient of the complex number 4-3i divided by its conjugate is:
(7 - 24i) / 25
what is quotient of the complex number 4-3i divided by its conjugate?
fraction
1 answer