Question

(-7 - sq.rt of -49) / (1 + sq.rt of -1) in the form of a+bi
can anyone help me figure this out?

Answer 1

Remember, \(\sf i\) = \(\sqrt{-1}\) , whereas \(\sf i^2\) = \(-1\)\[\dfrac{-7 -\sqrt{-49}}{1+\sqrt{-1}}\] Simplifying the bottom, we can replace \(\sqrt{-1}\) with one of our identities. \[\frac{-7-\sqrt{-1}\sqrt{49}}{1+i}\]Here, we can replace the \(\sqrt{-1}\) with our identity once again. \[\frac{-7-i\sqrt{49}}{1+i}\]Reduce \(\sqrt{49}\)\[\frac{-7 -7i}{1+i}\]factor out like terms. \[\frac{-7(1+i)}{1+i}\] reduce this function by canceling out like terms and you will have your answer :)