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# How would you simplify 2/3-i?

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.

### 2 Answers by Expert Tutors

Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
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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.
Jason S. | My goal is the success of my students. Knowledge-Patience-HonestyMy goal is the success of my students. K...
4.9 4.9 (115 lesson ratings) (115)
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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.