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Leno4ka [110]
2 years ago
14

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

Mathematics
1 answer:
Dmitry_Shevchenko [17]2 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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Step-by-step explanation:

1.

Simplify the expression by combining like terms. Remember, like terms have the same variable part, to simplify these terms, one performs operations between the coefficients. Please note that a variable with an exponent is not the same as a variable without the exponent. A term with no variable part is referred to as a constant, constants are like terms.

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Use a very similar method to solve this problem as used in the first. Please note that all of the rules mentioned in the first problem also apply to this problem; for that matter, the rules mentioned in the first problem generally apply to any pre-algebra problem.

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Use the same rules as applied in the first problem. Also, keep the distributive property in mind. In simple terms, the distributive property states the following (a(b+c)=(a)(b)+(a)(c)=ab+ac). Also note, a term raised to an exponent is equal to the term times itself the number of times the exponent indicates. In the event that the term raised to an exponent is a constant, one can simplify it. Apply these properties here,

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The same method used to solve problem (3) can be applied to this problem.

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