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Leno4ka [110]
3 years ago
14

Simplify: 8i^7+6i^5-5i^3-3i^2-7i-9

Mathematics
1 answer:
Dmitry_Shevchenko [17]3 years ago
5 0
<span>Consider the remainder of the division of the power exponent of i by 4.
For a remainder r equal to 0, 1, 2 or 3, we have a power equal to 1, i, -1 or -i respectively, therefore:

</span>8i^7+6i^5-5i^3-3i^2-7i-9 =
8*(-i) + 6*i - 5*(-i) - 3*(-1) - 7i - 9 =
- 8i + 6i + 5i + 3 - 7i - 9 =
3 - 9 - 8i + 6i + 5i- 7i =
=\boxed{- 6 - 4i}

Answer:
\boxed{- 6 - 4i}

<span>

</span>
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