Question

Evaluate the following:
${( {i}^{18} + ( { \frac{1}{i} })^{25})}^{3}$​

Answer 1

Evaluation :

$\longmapsto{ \bigg( {i}^{18} + \big( { \frac{1}{i} } \big)^{25} \bigg)}^{3}$

$\longmapsto {\bigg( {i}^{16} \times {i}^{2} + \frac{1}{ {i}^{24} \times i } \bigg)}^{3}$

$\longmapsto {\bigg(( - 1) + \frac{1}{ {i} } \bigg) }^{3}$

$\longmapsto \bigg( - 1 - \frac{1}{i } + \frac{3}{i} + 3 \bigg)$

$\longmapsto \bf 2 \bigg(1 + \frac{1}{i} \bigg)$