Question

Examine the fraction 3+2i4−2i. Which expression is the first step to simplify the fraction? 3+2i4−2i⋅3−2i3−2i

3+2i4−2i⋅3+2i3+2i
3+2i4−2i⋅4−2i4−2i
3+2i4−2i⋅4+2i4+2i

Answer 1

The correct answer is the last option.

Explanation:

When you have a fraction with complex numbers, the first step to simplify is to multiply up and down the conjugate of the denominator, this will eliminate the complex part of the denominator, and in this way you can separate the expression in its real and complex part.

For the expression:

`(3 + 2i)/(4-2i )`

The denominator conjugate is 4 + 2i

When multiplied, the denominator is:

`4 ^ 2 -4i ^ 2 = 16 -4 (-1) = 20`