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Why is 1/(1+i) = 1/2 +- 1/2*i?

 Nov 14, 2016
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LEFT HAND SIDE:

 

Simplify the following:
1/(1+i)

Multiply numerator and denominator of 1/(1+i) by 1-i:
(1-i)/((1+i) (1-i))

(1+i) (1-i) = 1×1+1 (-i)+i×1+i (-i) = 1-i+i+1 = 2:
Answer: |(1-i)/2

 

RIGHT HAND SIDE:

 

Simplify the following:
1/2-(i)/(2)
1/2-(i)/2 = (1-i)/2:
Answer: |(1-i)/2

 Nov 14, 2016

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