Do you know i i ?

Algebra Level 1

Using your knowledge of the imaginary unit i i evaluate the following:

i 3296 {i}^{3296}


The answer is 1.

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Isaiah Simeone by isaiah simeone , 23, Australia

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2 solutions

Isaiah Simeone
Sep 27, 2014

i 3296 {i}^{3296}

We know that for any exponent divisible by 4, i i is 1.

The last two digits of 3296 is 96 which is divisible by 4.

therefore, i 3296 = 1 i^{3296}=1

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Ashish Menon
Jun 2, 2016

3296 ≡ 0 ( mod 4 ) 3296 \equiv 0 \left(\text{mod 4}\right)
So, i 3296 = 1 i^{3296} = \color{#69047E}{\boxed{1}}

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