Question 984827
{{{(3*(cos(60)+i*sin(60)))^4}}}



{{{(3)^4*(cos(4*60)+i*sin(4*60))}}} Use De Moivre's Theorem



{{{81*(cos(240)+i*sin(240))}}}



{{{81*(-1/2+i*(-sqrt(3)/2))}}} Use a unit circle or trig table



{{{81*(-1/2)+81*i*(-sqrt(3)/2)}}}



{{{-81/2-((81*sqrt(3))/2)i}}}



{{{-40.5-70.14806i}}}



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The exact answer as a fraction is {{{-81/2-((81*sqrt(3))/2)i}}}. Notice it is in the form {{{a+bi}}} where {{{a = -81/2}}} and {{{b = -(81*sqrt(3))/2}}}



The approximate answer is {{{-40.5-70.14806i}}}. Notice it is in the form {{{a+bi}}} where {{{a = -40.5}}} and {{{b = -70.14806}}} (rounded to 5 decimal places)