Question 171035
you need to remove the 1-i from the denominator.
here's how:
multiply numerator and denominator by (1+i)
your equation becomes:
{{{(2i*(1+i))/((1-i)*(1+i))}}}
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when you multiply {{{(1-i)*(1+i)}}} you get:
{{{1 - i + i - i^2}}}
which becomes:
{{{1 - i^2}}}
since {{{i^2 = -1}}}, it becomes:
{{{1 - (-1)}}}
which becomes:
{{{2}}}
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the denominator of your equation is 2
the numerator is:
{{{2i*(1+i)}}}
when you multiply that out, you get:
{{{2i + 2i^2}}}
since i^2 = -1, that becomes:
{{{2i + 2*(-1)}}}
which becomes
{{{2i -2}}}
your equation is now:
{{{(2i-2)/2}}}
simplify by dividing the numerator by the denominator to get:
{{{i-1}}}
put in standard complex form with the real part first and the imaginary part last:
{{{-1+i}}}
and you're done.
the answer is:
{{{-1+i}}}