Answer to Question #349061 in Complex Analysis for Mapula Advice

Question #349061

Express 2i/1+i in the form a+bi, where



a,b∈R.


1
Expert's answer
2022-06-13T14:44:12-0400

Multiply the numerator and denominator by "\\overline{1+i}=1-i":

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


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