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Express $\dfrac{30+19i}{4+9i}$ in the form $a + bi$, where $a$ and $b$ are real numbers.

Guest Jan 14, 2018
 #1
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\($\dfrac{30+19i}{4+9i}$\)       multiply top/bottm by  4  - 9i

 

[ 30  +  19i ] [ 4 - 9i ]  / (  4 + 9i) (4 - 9i) ]

 

[ 120 + 76i  - 270i   -  171i^2 ]  /  [ 16 -  81i^2  ]

 

[  120  +  171  -  194i ]  /  [ 16 + 81  ]

 

[ 291  -  194i  ] / [ 97 ]

 

(291/ 97)  -  (194/97) i

 

3 - 2i

 

 

cool cool cool

CPhill  Jan 15, 2018

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