Simplify 13 over the quantity of negative 3 plus 2i.

13

-

3

+

2

i

Multiply by

-

3

-

2

i

-

3

-

2

i

to make the denominator of

13

-

3

+

2

i

real.

13

-

3

+

2

i

-

3

-

2

i

-

3

-

2

i

Combine.

13

(

-

3

-

2

i

)

(

-

3

+

2

i

)

(

-

3

-

2

i

)

Expand

(

-

3

+

2

i

)

(

-

3

-

2

i

)

using the FOIL Method.

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13

(

-

3

-

2

i

)

-

3

⋅

-

3

-

3

(

-

2

i

)

+

2

i

⋅

-

3

+

2

i

(

-

2

i

)

Simplify.

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13

(

-

3

-

2

i

)

9

-

4

i

2

Simplify each term.

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13

(

-

3

-

2

i

)

9

+

4

Reduce the expression by cancelling the common factors.

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-

3

-

2

i