Question

(a + b)(a - b) = a^2 - b^2

1. Multiply the numerator and the denominator by the complex conjugate of the denominator.

2. Simplify the results into the real part and the imaginary part.

Divide the complex numbers. Show all work.

Answer 1

Explanation:

hello : given z = (-6-10i)/(4+7i)

the complex conjugate of the denominator is : 4-7i

1. Multiply the numerator and the denominator by the complex conjugate of the denominator: z = (-6-10i)(4-7i)/(4+7i)(4-7i)

use identity : (a + b)(a - b) = a² - b² calculate the product : (4+7i)(4-7i)

(4+7i)(4-7i) = 4² -(7i)² =16 -49i² =16+49 = 65..... ( i² = -1)

2) Simplify the results calculate the numerator : (-6-10i)(4-7i)

(-6-10i)(4-7i) = -24+42i -40i+70i² = -24+42i -40i-70 .....( i² = -1)

(-6-10i)(4-7i) = -94+2i

now : z = (-94+2i )/65 = (-94/65) +(2/65) i

the real part is : ( -94/65) and the imaginary part is : 2/65