Question

Which expression is correct for question 7

Answer 1

◆ COMPLEX NUMBERS ◆


`given \: expression \: is \: - \\ \\ - 3 {i}^(4) + 2 {i}^(3) + 2 {i}^(2) + √( - 9) \\ \\ we \: know \: that \: , \: \\ i = √( - 1) \\ \\ {i}^(2) = - 1 \\ \\ {i}^(3 ) = - i \\ \\ {i}^(4) = 1 \\ \\ \\ - 3 {i}^(4) + 2 {i}^(3) + 2 {i}^(2) + √(9) i \\ = - 3 {i}^(4) + 2 {i}^(3) + 2 {i}^(2) + 3i \\ \\ using \: the \: above \: properties \: of \: iota \: (i) \\ \\ = - 3(1) + 2( - i) + 2( - 1) + 3i \\ \\ = - 3 - 2i - 2 + 3i \\ \\ = (- 5 + i) \: \: \: ans.`