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i^50
<-- Enter i raised to a power such as i^4 or a coefficient and i raised to a power such as 6i^7 or a product such as 3i^4 * 8i^6
We need to evaluate and simplify i
^{50}
where i = √
-1
Since the power you entered of 50 is greater 4, then we see how many i
^{4}
factors we can factor out:
i
^{50}
= (i
^{48}
)(i
^{2}
)
i
^{50}
= ((i
^{4}
)
^{12}
)(i
^{2}
)
First calculate i
^{4}
:
i
^{4}
= √
-1
* √
-1
* √
-1
* √
-1
i
^{4}
= (√
-1
)
^{2}
* (√
-1
)
^{2}
i
^{4}
= -1 * -1
i
^{4}
= 1
Now substitute our i
^{4}
value back in the equation:
i
^{ 50}
= (1
^{12}
)(i
^{2}
) <--- i
^{4}
= 1
i
^{ 50}
= 1(i
^{2}
)
Now calculate i
^{2}
:
i
^{2}
= √
-1
* √
-1
i
^{2}
= √
-1
^{2}
i
^{2}
= -1
Now, finish up and evaluate our product:
i
^{50}
= 1 * -1 <--- i
^{2}
= -1
i
^{50}
= -1
i
^{50}
=
-1