Question

PLZ ANSWER THIS QUESTION I WILL GIVE BRAINLIEST THE ONE WHO WILL BE RIGHT​

Answer 1

Step-by-step explanation:

Given :-

(i⁵⁹² + i⁵⁹⁰ + i⁵⁸⁸ + i⁵⁸⁶ + i⁵⁸⁴)/(i⁵⁸²+i⁵⁸⁰+i⁵⁷⁸+i⁵⁷⁴)

To find :-

Find the value of the expression:

(i⁵⁹² + i⁵⁹⁰ + i⁵⁸⁸ + i⁵⁸⁶ + i⁵⁸⁴)/(i⁵⁸²+i⁵⁸⁰+i⁵⁷⁸+i⁵⁷⁴) ?

Solution:-

Given that

(i⁵⁹² + i⁵⁹⁰ + i⁵⁸⁸ + i⁵⁸⁶ + i⁵⁸⁴)/(i⁵⁸²+i⁵⁸⁰+i⁵⁷⁸+i⁵⁷⁴)

i⁵⁹² can be written as i⁵⁸⁴ × i⁸

i⁵⁹⁰ can be written as i⁵⁸⁴ × i⁶

i⁵⁸⁶ can be written as i⁵⁸⁴ × i²

i⁵⁸² can be written as i⁵⁷⁴ × i⁸

i⁵⁸⁰ can be written as i⁵⁷⁴ × i⁶

i⁵⁷⁸ can be written as i⁵⁷⁴ × i²

Since a^m × a^n = a^(m+n)

=> (i⁵⁹² + i⁵⁹⁰ + i⁵⁸⁸ + i⁵⁸⁶ + i⁵⁸⁴)/(i⁵⁸²+i⁵⁸⁰+i⁵⁷⁸+i⁵⁷⁴)

=> (i⁵⁸⁴×i⁸+i⁵⁸⁴×i⁶+i⁵⁸⁴×i²+i⁵⁸⁴) /(i⁵⁷⁴×i⁸+i⁵⁷⁴×i⁶+i⁵⁷⁴×i²+i⁵⁷⁴)

=>[i⁵⁸⁴( i⁸+i⁶+i²+1)]/ [i⁵⁷⁴(i⁸+i⁶+i²+1)]

On cancelling i⁸+i⁶+i²+1 in both the numerator and the denominator then

=> i⁵⁸⁴/i⁵⁷⁴

=> i^584-574)

Since a^m/a^n = a^(m-n)

=> i¹⁰

=> (i²)⁵

Since (a^m)^n = a^(mn)

=> (-1)⁵

Since i² = -1

=> -1×-1×-1×-1×-1

=> -1

Answer:-

The value of the expression

(i⁵⁹²+i⁵⁹⁰+i⁵⁸⁸+i⁵⁸⁶+i⁵⁸⁴)/(i⁵⁸²+i⁵⁸⁰+i⁵⁷⁸+i⁵⁷⁴) is -1

Used formulae:-

• a^m × a^n = a^(m+n)
• a^m/a^n = a^(m-n)
• (a^m)^n = a^(mn)
• i² = -1

Answer 2

Answer:

Step-by-step explanation:

Given :-

(i⁵⁹² + i⁵⁹⁰ + i⁵⁸⁸ + i⁵⁸⁶ + i⁵⁸⁴)/(i⁵⁸²+i⁵⁸⁰+i⁵⁷⁸+i⁵⁷⁴)

To find :-

Find the value of the expression:

(i⁵⁹² + i⁵⁹⁰ + i⁵⁸⁸ + i⁵⁸⁶ + i⁵⁸⁴)/(i⁵⁸²+i⁵⁸⁰+i⁵⁷⁸+i⁵⁷⁴) ?

Solution:-

Given that

(i⁵⁹² + i⁵⁹⁰ + i⁵⁸⁸ + i⁵⁸⁶ + i⁵⁸⁴)/(i⁵⁸²+i⁵⁸⁰+i⁵⁷⁸+i⁵⁷⁴)

i⁵⁹² can be written as i⁵⁸⁴ × i⁸

i⁵⁹⁰ can be written as i⁵⁸⁴ × i⁶

i⁵⁸⁶ can be written as i⁵⁸⁴ × i²

i⁵⁸² can be written as i⁵⁷⁴ × i⁸

i⁵⁸⁰ can be written as i⁵⁷⁴ × i⁶

i⁵⁷⁸ can be written as i⁵⁷⁴ × i²

Since a^m × a^n = a^(m+n)

=> (i⁵⁹² + i⁵⁹⁰ + i⁵⁸⁸ + i⁵⁸⁶ + i⁵⁸⁴)/(i⁵⁸²+i⁵⁸⁰+i⁵⁷⁸+i⁵⁷⁴)

=> (i⁵⁸⁴×i⁸+i⁵⁸⁴×i⁶+i⁵⁸⁴×i²+i⁵⁸⁴) /(i⁵⁷⁴×i⁸+i⁵⁷⁴×i⁶+i⁵⁷⁴×i²+i⁵⁷⁴)

=>[i⁵⁸⁴( i⁸+i⁶+i²+1)]/ [i⁵⁷⁴(i⁸+i⁶+i²+1)]

On cancelling i⁸+i⁶+i²+1 in both the numerator and the denominator then

=> i⁵⁸⁴/i⁵⁷⁴

=> i^584-574)

Since a^m/a^n = a^(m-n)

=> i¹⁰

=> (i²)⁵

Since (a^m)^n = a^(mn)

=> (-1)⁵

Since i² = -1

=> -1×-1×-1×-1×-1

=> -1

Answer:-

The value of the expression

(i⁵⁹²+i⁵⁹⁰+i⁵⁸⁸+i⁵⁸⁶+i⁵⁸⁴)/(i⁵⁸²+i⁵⁸⁰+i⁵⁷⁸+i⁵⁷⁴) is -1

Used formulae:-

a^m × a^n = a^(m+n)

a^m/a^n = a^(m-n)

(a^m)^n = a^(mn)

i² = -1