Question

Evaluate:
$(i {}^{37} + \frac{1}{i {}^{67} } )$
Correct answer required ​

Answer 1

Answer:

the answer is

Step-by-step explanation:

=>i

37

=>(i

2

)

18

×i

=>−1

18

×

−1

=>

−1

=>i

\begin{lgathered}\\ \\ \\ = > {i}^{67} \\ \\ = > {( {i}^{2} )}^{33} \times i \\ \\ = > { - 1}^{33} \times \sqrt{ - 1} \\ \\ = > - \sqrt{ - 1} \\ \\ = > - i\end{lgathered}

=>i

67

=>(i

2

)

33

×i

=>−1

33

×

−1

=>−

−1

=>−i

\begin{lgathered}\\ \\ \\ = > {i}^{37} + \frac{1}{ {i}^{67} } \\ \\ = > i + \frac{1}{ {( - i)}^{2} } \\ \\ = > i - \frac{1}{ {i}^{2} } \\ \\ = > \frac{{i}^{3} - 1 }{ - 1} \\ \\ = > - {i}^{3} + 1 \: or \: 1 - {i}^{3}\end{lgathered}

=>i

37

+

i

67

1

=>i+

(−i)

2

1

=>i−

i

2

1

=>

−1

i

3

−1

=>−i

3

+1or1−i

3

Answer 2

$refer \: to \: attachment \: \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ hope \: its \: help \: u$