document.write( "Question 171035: how can I solve this problem?\r
\n" ); document.write( "\n" ); document.write( " 2i
\n" ); document.write( " ______
\n" ); document.write( " 1-i \n" ); document.write( "

Algebra.Com's Answer #126248 by gonzo(654) $\"\"$ $\"About$

You can put this solution on YOUR website!
you need to remove the 1-i from the denominator.
\n" ); document.write( "here's how:
\n" ); document.write( "multiply numerator and denominator by (1+i)
\n" ); document.write( "your equation becomes:
\n" ); document.write( " $\"%282i%2A%281%2Bi%29%29%2F%28%281-i%29%2A%281%2Bi%29%29\"$
\n" ); document.write( "-----
\n" ); document.write( "when you multiply $\"%281-i%29%2A%281%2Bi%29\"$ you get:
\n" ); document.write( " $\"1+-+i+%2B+i+-+i%5E2\"$
\n" ); document.write( "which becomes:
\n" ); document.write( " $\"1+-+i%5E2\"$
\n" ); document.write( "since $\"i%5E2+=+-1\"$ , it becomes:
\n" ); document.write( " $\"1+-+%28-1%29\"$
\n" ); document.write( "which becomes:
\n" ); document.write( " $\"2\"$
\n" ); document.write( "-----
\n" ); document.write( "the denominator of your equation is 2
\n" ); document.write( "the numerator is:
\n" ); document.write( " $\"2i%2A%281%2Bi%29\"$
\n" ); document.write( "when you multiply that out, you get:
\n" ); document.write( " $\"2i+%2B+2i%5E2\"$
\n" ); document.write( "since i^2 = -1, that becomes:
\n" ); document.write( " $\"2i+%2B+2%2A%28-1%29\"$
\n" ); document.write( "which becomes
\n" ); document.write( " $\"2i+-2\"$
\n" ); document.write( "your equation is now:
\n" ); document.write( " $\"%282i-2%29%2F2\"$
\n" ); document.write( "simplify by dividing the numerator by the denominator to get:
\n" ); document.write( " $\"i-1\"$
\n" ); document.write( "put in standard complex form with the real part first and the imaginary part last:
\n" ); document.write( " $\"-1%2Bi\"$
\n" ); document.write( "and you're done.
\n" ); document.write( "the answer is:
\n" ); document.write( " $\"-1%2Bi\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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