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Express 1/(1 + 1/(1 + i)) in the form a + bi, where a and b are real numbers.

 Jan 9, 2022
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First: simplify  1 / (1 + i)  by multiplying both the numerator and denominator by the conjugate of the denominator.

 

The conjugate of  1 + i  is  1 - i.

 

1 / (1 + i)  x  (1 - i) / (1 - i)  =  (1 - i) / 2

 

You now have:  1 / ( 1 + (1 - i) / 2 )  =  1 / ( 1 + 1/2 - i/2 )  =  1 / ( 3/2 - i/2 )

 

Simplify by multiplying both the numerator and denominator by the conjugate of the denominator.

 

1 / ( 3/2 - i/2 )  x  ( 3/2 + i/2 ) / ( 3/2 + i/2 )  =  (3/2 + i/2) / 2.5  =  0.6 + 0.2i

 Jan 9, 2022

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