Fun with imaginary numbers

Algebra Level 1

Find the sum of the imaginary numbers above.

Note: i 1 = i , i 2 = − 1 , i 3 = − i , i 4 = 1 { i }^{ 1 }=i,{ i }^{ 2 }=-1,{ i }^{ 3 }=-i,{ i }^{ 4 }=1


The answer is 1.

Rhiana Vanessa Bag-id Amoin by Rhiana Vanessa Bag-id Am… , 25

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2 solutions

Azadali Jivani
Aug 11, 2015

i^2844 + i^4689 + i^3683 = ?
So it is i^0 + i^1 + i^3 = 1 + i -i = 1 (Ans.)

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= i^2884+(i^4688)(i^1)+(i^3680)(i^3) = 1+(1)(i)+(1)(-i) = 1+i-i = 1

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