Question

What answer is this?

Answer 1

option B

`(31)/(50)-(4)/(25) i`

Explanation:

Given in the question a complex fraction

Step1

To divide complex numbers, you must multiply by the conjugate. To find the conjugate of a complex number all you have to do is change the sign between the two terms in the denominator.

`(5+4i)/(6+8i)((6-8i)/(6-8i))`

Step2

Distribute (or FOIL) in both the numerator and denominator to remove the parenthesis.

`(30+24i-40i-32i²)/(36-64i^(2) )`

Step3

Simplify the powers of i, specifically remember that i² = –1.

`(62-16i)/(36+64)`

Step4

`(62)/(100)-(16i)/(100)`

Step5

simply

`(31)/(50)-(4)/(25)i`