Question 407765
{{{(1+j)^24 = (sqrt(2)*(sqrt(2)/2 + j(sqrt(2)/2)))^24

= 2^12(cos(pi/4) + j*sin(pi/4))^24

=2^12(cos(6pi) + j*sin(6pi))}}}, using de Moivre's Theorem.

Hence
{{{(1+j)^24 = 2^12 (1 + j*0) = 2^12}}}.

Now, {{{2^24 = ((1-j)(1+j))^24 = (1-j)^24(1+j)^24 = 2^12(1-j)^24}}}
==> {{{2^24 = 2^12(1-j)^24}}}
==> {{{2^12 = (1-j)^24}}}