Question 661877
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Hi, there-

Your Question:
Simplify {{{(i(1+i)^12)/(((1+i)^12)-1)}}}

Answer:
The imaginary number i is so much fun to play with! (OK, maybe that's too nerdy)

Remember, 
{{{i=sqrt(-1)}}}
{{{i^2=-1}}}

So, using exponent laws, we have,
{{{(1+i)^2=(1+i)(1+i)=1+2i-1=2i}}}
{{{(1+i)^4 =(1+i)^2(1+i)^2=(2i)(2i)=(4)(-1)=-4}}}
{{{(1+i)^12=(1+i)^4(1+i)^4(1+i)^4=(-4)(-4)(-4)=-64}}}

{{{(i(1+i)^12)/(((1+i)^12)-1)=(i*(-64))/(-64-1)=64i/65}}}

~Mrs. Figgy
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