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

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Answer 1 · 2018-01-05T08:11:14

$i$

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

$((1+i)/(1-i))*((1+i)/(1+i)) = (1+2i+i^2)/(1-i^2)$

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

$(1+2i+i^2)/(1-i^2) = (1+2i-1)/(1-(-1)) =(2i)/2=i$ .

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