SOLUTION: Express $\frac 1{1+\frac 1{1-\frac 1{1+i}}}$ in the form $a+bi$, where $a$ and $b$ are real numbers. In case you have trouble reading that, here's the same expression written wi

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Express $\frac 1{1+\frac 1{1-\frac 1{1+i}}}$ in the form $a+bi$, where $a$ and $b$ are real numbers. In case you have trouble reading that, here's the same expression written wi      Log On


   

Question 1189371: Express $\frac 1{1+\frac 1{1-\frac 1{1+i}}}$ in the form $a+bi$, where $a$ and $b$ are real numbers.
In case you have trouble reading that, here's the same expression written with the other type of fraction notation: 1/(1+1/(1-1/(1+i))).
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Express $\frac 1{1+\frac 1{1-\frac 1{1+i}}}$ in the form $a+bi$, where $a$ and $b$ are real numbers.
In case you have trouble reading that, here's the same expression written with the other type of fraction notation: 1/(1+1/(1-1/(1+i))).
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This is just grinding it out.
Work right to left.
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To start:
1/(1+i)
Multiply the DEN and the NUM by the conjugate of the DEN.
= (1-i)/((1+i)*(1-i) = (1-i)/2