Question

2i7 +6i9 +7i18–3i16 +4i24

Answer 1

SOLUTION

TO DETERMINE

The value of

$\sf{2 {i}^{7} + 6 {i}^{9} + 7{i}^{18} - 3{i}^{16} + 4{i}^{24}}$

CONCEPT TO BE IMPLEMENTED

We know i is a complex number so that i² = - 1

EVALUATION

$\sf{2 {i}^{7} + 6 {i}^{9} + 7{i}^{18} - 3{i}^{16} + 4{i}^{24}}$

$\sf{ = 2 {( {i}^{2} )}^{3} .i+ 6 {( {i}^{2} )}^{4} .i + 7{( {i}^{2} )}^{9} - 3{( {i}^{2} )}^{8} + 4{( {i}^{2} )}^{12} }$

$\sf{ = 2 {( - 1 )}^{3} .i+ 6 {( - 1)}^{4} .i + 7{( - 1)}^{9} - 3{( - 1 )}^{8} + 4{( - 1 )}^{12} }$

$\sf{ = - 2 i+ 6 i - 7 - 3 + 4}$

$\sf{ = - 6 + 4 i }$

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