How do you calculate $\frac{1 + i}{1 - i}$ $(1+i)/(1-i)$ ?

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Answer 1 · 2018-01-05T08:11:14

$i$ $i$

We can compute this by multiplying both numerator and denominator by the conjugate, $1 + i$ $1+i$ , of the denominator.

$(\frac{1 + i}{1 - i}) \cdot (\frac{1 + i}{1 + i}) = \frac{1 + 2 i + i^{2}}{1 - i^{2}}$ $((1+i)/(1-i))*((1+i)/(1+i)) = (1+2i+i^2)/(1-i^2)$

We know that $i^{2} = - 1$ $i^2=-1$ , so:

$\frac{1 + 2 i + i^{2}}{1 - i^{2}} = \frac{1 + 2 i - 1}{1 - (- 1)} = \frac{2 i}{2} = i$ $(1+2i+i^2)/(1-i^2) = (1+2i-1)/(1-(-1)) =(2i)/2=i$ .

How do you calculate (1+i)/(1-i)1+i1−i(1+i)/(1-i)?