Question

Which expression is equivalent to (StartRoot 3 EndRoot + i) cubed? URGENT!!!!!!!!!! WILL GIVE BRAINLIEST

Answer 1

Answer:

third option

Step-by-step explanation:

Using De Moivre's theorem

($\sqrt{3}$ + i)³ , then

| $\sqrt{3}$ + i |

= $\sqrt{(\sqrt{3})^2+1^2 }$

= $\sqrt{3+1}$ = $\sqrt{4}$ = 2

arg($\sqrt{3}$ + i) = $tan^{-1}$( $\frac{1}{\sqrt{3} }$ ) = $\frac{\pi }{6}$

Thus

($\sqrt{3}$ + i)³

= 2³ [ cos(3 ×$\frac{\pi }{6}$ ) + isin( 3 × $\frac{\pi }{6}$ ) ]

= 8 [ cos($\frac{\pi }{2}$) + isin($\frac{\pi }{2}$ ) ]