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Express (2 + i)/(4 + i - 3 + 6i) in the form a + bi, where a and b are real numbers.

 Jan 9, 2022
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First:  simplify  4 + i - 3 + 6i  =  7i + 1

 

Then:  to simplify  (2 + i ) / (7i + 1)  multiply both the numerator and denominator by the conjugate of the denominator.

 

The conjugate of  7i + 1  is  7i - 1.

 

(2 + i ) / (7i + 1)   x   (7i - 1) / (7i - 1)  =  [ (2 + i)(7i - 1) ] / [ (7i + 1)(7i - 1) ]

                                                          =  ( 13i - 9) / -50

                                                          =  -(13/50)I + (9/50)

 Jan 9, 2022

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