Question

Show that (-1+ √3 i)^3 is a real number.​

Answer 1

Answer:

$( - 1 + \sqrt{3} i) {}^{3} = ( - 1) {}^{3} + {( \sqrt{3}i) }^{3} + 3 {( - 1)}^{2} \sqrt{3} i + 3( - 1) {( \sqrt{3} i)}^{2} \\ - 1 - 3 \sqrt{3} i + 3 \sqrt{3} i + 9 = 8 \\ (real \: number). \: proved$