Question

Find the quotient of these complex numbers. (6-i) divided by (4+3i)=

a) (1/8) - (3/8)i
b) (1/8) + (3/8)i
c) (3/8) - (1/8)i
d) (3/8) + (1/8)i

Answer 1

The quotient of the complex numbers (6 - i) / (4 + 3i) is (21/25) - (6/25)i.

Step-by-step explanation:

To find the quotient of the complex numbers (6-i) divided by (4+3i), we first multiply the numerator and the denominator by the conjugate of the denominator to eliminate the imaginary part in the denominator. To find the quotient of complex numbers, we can use the formula:

(a + bi) / (c + di) = [(a * c + b * d) / (c^2 + d^2)] + [(b * c - a * d) / (c^2 + d^2)]i

In this case, we have (6 - i) / (4 + 3i). Substituting the values, we get:

(6 * 4 + (-1) * 3) / (4^2 + 3^2) + ((-1) * 4 - 6 * 3) / (4^2 + 3^2)i

Simplifying the equation gives us:

21/25 - 6/25i

Therefore, the quotient of the complex numbers is (21/25) - (6/25)i, which corresponds to option a) (1/8) - (3/8)i.