How do you simplify $i^{247}$ $i^247$ ?

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Answer 1 · 2016-01-19T19:09:21

A great trick to solving this type of problem is understanding that there are only 4 possible solution ...

Raising the imaginary number $i$ $i$ to a power can only result in 4 possible solutions :

$i^{0} = 1$ $i^0=1$
$i^{1} = i$ $i^1=i$
$i^{2} = - 1$ $i^2=-1$
$i^{3} = - i$ $i^3=-i$

Here's the trick ... divide the exponent by the number 4 and calculate the remainder. Then, use the remainder as the new exponent .

In this example, $\frac{247}{4} = 61 with remainder 3$ $247/4=61 " with remainder " 3$

Answer: $i^{247} = i^{3} = - i$ $i^247=i^3=-i$

hope that helped

How do you simplify i247i^247?