Question

express each of the complex number in the from of ..(a+ib)......(1)(⅓+3i)³.....(2) (-2-⅓i)³​

Answer 1

Answer:

${( \frac{1}{3} + 3i)}^{3} \\ = {( \frac{1}{3} )}^{3} + {(3i)}^{3} + 3 ( { \frac{1}{3} )}^{2} 3i \: + 3( \frac{1}{3} )( {3i)}^{2} \\ = \frac{1}{27} + 27 {i}^{3} + i + 9 {i}^{2} \\ = \frac{1}{27} - 27i + i - 9 \\ \frac{ = 246}{27} - 26i$