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

Note:

4 +i . 5 - i =

5 +i 5 - i

20 +5i-4i +1 =

25 + 1

21 + i

26 26

To divide 2 complex numbers .

Multiply the denominator by its conjugate, i.e. 5+i , by 5- i

the denominator becomes real number, i.e. 26

and the result is a complex number with real , and imaginary part.

4 + i

------

5 + i

Multiply top and bottom by the conjugate, 5-i.

(4+i)(5-i)

-----------

(5+i)(5-i)

Using FOIL (first outside inside last)

20 - 4i + 5i - i^{2}

-----------------

25 -5i + 5i - i^{2}

20 + i - (-1)

--------------

25 - (-1)

20+1 + i

------------

25+1

John M. | John - Algebra TutorJohn - Algebra Tutor

Division of Complex Numbers:

1) Find the conjugate of the denominator. The conjugate of a complex number is simply the same expression with the opposite sign. In this case the conjugate of 5+i is 5-i.

2) Multiply the given fraction by the conjugate fraction.

(4+i) (5-i) 20-4i+5i-i^{2}

------ x ------- = -------------- , you can see that this new fraction simplifies quite a bit

(5+i) (5-i) 25+5i-5i-i^{2}

3) Simplify the fraction, i^{2} =-1, and add the common terms (5i-4i=i, 5i-5i=0)

20+i+1 21+i

---------- = ---------

25+1 26

That is the final answer.

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