Question

Evaluate: [i¹⁸+(1/i)²⁵]³
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Answer 1

Answer:

$- 1 + i$

Step-by-step explanation:

$sol {}^{n}$

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

$= (i {}^{2} ) {}^{9} + \frac{1 {}^{25} }{i {}^{25} } ) {}^{3}$

$= (( - 1) {}^{9} + \frac{1}{ - i} )$

$= ( - 1 + \frac{1 \times i}{ - i \times i} )$

$= ( - 1 + \frac{i}{ - i {}^{2} } )$

$= ( - 1 - \frac{i}{ - 1} )$

$= ( - 1 + i)$

$= - 1 + i$