Question

Value of i^-888

Please help me ​

Answer 1

Answer:

$\longrightarrow\Large\boxed{1}$

Step-by-step explanation:

GIVEN:

i⁻⁸⁸⁸ (find the value.)

To solve this problem, first you have to find the value of i⁻⁸⁸⁸ to isolate by the i from one side of the equation.

SOLUTIONS:

First, thing you do is exponent rule.

$\Large\boxed{\textnormal{EXPONENTS RULE FORMULA}}$

$\displaystyle \mathsf{A^-^B=\frac{1}{A^B} }$

Solve.

$\displaystyle \mathsf{\frac{1}{i^{888}}}$

$\mathsf{\textnormal{EXPONENT RULES}}$

$\mathsf{A^B^C=(A^B)^C}$

$\displaystyle \mathsf{i^{888}=(i^2)^4^4^4}$

Rewrite as a fraction.

$\displaystyle \mathsf{\frac{1}{(i^2)^{444}}}$

Used imaginary number line rule.

$\Large\boxed{\textnormal{IMAGINARY NUMBER LINE RULES FORMULA}}$

$\mathsf{i^2=-1}$

$\displaystyle\mathsf{\frac{1}{(-1)^{444}}}}$

$\mathsf{EXPONENT\quad RULES}$

$\displaystyle \mathsf{(-A)^N=A^N}}$

$\displaystyle\mathsf{(-1)^4^4^4=1^4^4^4}$

Rewrite as a fraction again.

$\displaystyle \mathsf{\frac{1}{1^{444}}}$

Solve with exponent and divide the numbers from left to right. (Simplify/ to find the answer.)

$\displaystyle \mathsf{1^4^4^4=1}$

Divide.

$\displaystyle \mathsf{\frac{1}{1}=\boxed{\mathsf{1}}} }$

$\Large\boxed{\mathsf{1}}$

In conclusion, the value of i⁻⁸⁸⁸ is 1, which is our answer.

Answer 2

Explanation:-

$\huge \boxed{i^{-888}=1}$

Given :-

$\iota^{-888}$

To find :-

It's required value.

Solution:-

As we know the iota is an imaginary number whose value is.

→$\iota = \sqrt{-1}$

• Similarly The value of :-

$\boxed{\iota^4 = 1 }$

• Let evulate this :-

→$\iota^{-888}$

• $\boxed{a^{-1} = \dfrac{1}{a}}$

• by using this we get,

→$\dfrac{1}{\iota^{888}}$

→$\dfrac{1}{(\iota^{4})^{222}}$

→$\dfrac{1}{1}$

→$1$

hence,

The required value is 1.