Answer:
see explanation
Step-by-step explanation:
Using De Moivre's theorem
Given
[ 4(cos15° + isin15° ) ]³, then
= 4³ [ cos(3 × 15°) + isin(3 × 15°) ]
= 64 (cos45° + isin45° )
= 64 ([tex]\frac{\sqrt{2} }{2}[/tex] + [tex]\frac{\sqrt{2} }{2}[/tex] i )
= 64 ([tex]\frac{\sqrt{2} }{2}[/tex] (1 + i) )
= 32[tex]\sqrt{2}[/tex] (1 + i)
= 32[tex]\sqrt{2}[/tex] + 32[tex]\sqrt{2}[/tex] i
