Question

Module Knowleoge Check Divide. (6-6i)/(2-5i) Write your answer as a complex number in standard

Answer 1

To divide complex numbers, we use a technique called complex conjugate.

Step-by-step explanation:

To divide complex numbers, we use a technique called complex conjugate. The complex conjugate of a complex number a+bi is obtained by changing the sign of its imaginary part, so the complex conjugate of 2-5i is 2+5i.

Then, we multiply both the numerator and denominator by the complex conjugate of the denominator.

(6-6i)/(2-5i) = ((6-6i)(2+5i))/((2-5i)(2+5i))

Expanding this expression gives us (12+30i-12i-30)/(4-10i+10i-25)

Simplifying further, we get (12+18i)/(29).

Therefore, (6-6i)/(2-5i) = 12/29 + 18i/29 as a complex number in standard form.