Question 1178087
First put it into exponential form:  {{{re^(i*theta) }}}
where r = {{{sqrt(a^2+b^2)}}} = {{{5*sqrt(2)}}}
and  {{{theta}}} = {{{tan^-1(b/a)}}} = {{{tan^-1(1) }}} = {{{45^o}}}

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Now {{{ (5+5i)^3 }}} = {{{ (5*sqrt(2))^3 * e^((3*45)*i) }}}

You can finish the calculation.

Once you have the answer in exponential form, you can write it in polar form (trivially) using this:  
{{{ r*e^(i*theta) = r*cos(theta)+i*r*sin(theta) }}}