I tried to multiply the 3-i on the top and bottom but then I get lost on what belongs on the bottom and on the top.

I thought I would have something like 6-2i/9 but that doesn't seem right.

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Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...

This is division of 2 complex numbers.

2__ =

3 - i

Multiply both numerator and denominator by conjugate number of the denominator.

2 * 3+ i =

3 - i 3 +i

separate the rational and irrational numbers from

each other

6 + 2i = 3 + 1 i

10 5 5

This is also division of 2 complex numbers into each other.

Multiply top and bottom by the conjugate, 3+i:

2 3 + i

--- * ------

3-i 3 + i

2(3+i)

--------

(3-i)(3+i)

6 + 2i

----------

9 + 3i - 3i - i^2

6 + 2i

-------

9 - (-1)

6+2i

------- or (3/5) + (1/5) i

10

(3/5) + (i/5) works as well.

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