The quotient of the complex number (13 - i)/(3 - i) is D. 4 + i
What is the quotient of the complex numbers?
To find the quotient of the complex number (13 - i)/(3 - i), we multiply both the numerator and the denominator by the complex conjugate of the denominator.
Since the denominator is 3 - 1, its complex conjugate is 3 + i.
So,multiplying both the numerator and denominator by this complex conjugate 3 + i, we have
(13 - i)/(3 - i) = (13 - i)/(3 - i) × (3 + i)/(3 + i)
= (13 - i)(3 + i)/[(3 - i)(3 + i)]
= (13 × 3 + 13 × i - i × 3 - i × i)/(3² - i²) (since (3² - i²) = (3 - i)(3 + i) difference of two squares)
= (39 + 13i - 3i - i²)/(3² - i²)
= (39 + 10i - (-1))/[9 - (-1)]
= (39 + 10i + 1)/[9 + 1]
= (40 + 10i)/10
= 4 + i
So, the quotient of the complex number (13 - i)/(3 - i) is D. 4 + i
Learn more about quotient of a complex number here:
https://brainly.com/question/17210443
#SPJ1
