Evaluate the expression ans write the result in theform a + bi (1-sqrt(-1))/(1+sqrt(-1))

Evaluate the expression ans write the result in theform a + bi
$\frac{1-\sqrt{-1}}{1+\sqrt{-1}}$
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Brendon Bentley
$\frac{1-\sqrt{-1}}{1+\sqrt{-1}}=\frac{1-\sqrt{1\ast \left({i}^{2}\right)}}{1+\sqrt{1\ast \left({i}^{2}\right)}}=\frac{1-i}{1+i}$
$=\frac{\left(1-i\right)\left(1-i\right)}{\left(1-i\right)\left(1+i\right)}=\frac{1-i-i+{i}^{2}}{1+i-i-{i}^{2}}=\frac{1-2i-1}{1+1}=\frac{-2i}{2}=-i$
key points:
1). ${i}^{2}=-1$
2).for complex fraction, multiplie the conjugate of the denominator.