Write (-3+i)^(4) in simplest a+bi form. Answer:

Recognize Complex Number: To solve (-3+i)^(4), we first need to recognize that we are raising a complex number to the fourth power. We can start by raising (-3+i) to the second power to simplify the expression step by step. (-3+i)^2 = (-3+i)(-3+i) = (-3)^2 + 2(-3)(i) + (i)^2 = 9 - 6i - 1 (since i^2 = -1) = 8 - 6iSquare to Simplify: Now we need to square the result of (-3+i)^2 to get (-3+i)^4. (8 - 6i)^2 = (8 - 6i)(8 - 6i) = 8^2 - 2(8)(6i) + (6i)^2 = 64 - 96i + 36(i^2) Since i^2 = -1, we replace i^2 with -1 to get: = 64 - 96i - 36 = 28 - 96iSquare Result for (-3+i)^4: We have now expressed (-3+i)^4 in the simplest a+bi form, which is 28 - 96i.

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Write
(-3+i)^(4) in simplest
a+bi form.
Answer:

Write $(-3+i)^{4}$ in simplest $a+b i$ form. $\newline$ Answer:

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Precalculus

Find the roots of factored polynomials

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Q. Write

(-3+i)^{4}

in simplest

a+b i

form.

\newline

Answer:

Recognize Complex Number: To solve $(-3+i)^{4}$ , we first need to recognize that we are raising a complex number to the fourth power. We can start by raising $(-3+i)^{2}$ to simplify the expression step by step. $(-3+i)^2 = (-3+i)(-3+i) = (-3)^2 + 2(-3)(i) + (i)^2$ $= 9 - 6i - 1 \text{ (since } i^2 = -1)$ $= 8 - 6i$
Square to Simplify: Now we need to square the result of $(-3+i)^2$ to get $(-3+i)^4$ . $\newline$ $(8 - 6i)^2 = (8 - 6i)(8 - 6i) = 8^2 - 2(8)(6i) + (6i)^2$ $\newline$ $= 64 - 96i + 36(i^2)$ $\newline$ Since $i^2 = -1$ , we replace $i^2$ with $-1$ to get: $\newline$ $= 64 - 96i - 36$ $\newline$ $= 28 - 96i$
Square Result for $(-3+i)^4$ : We have now expressed $(-3+i)^4$ in the simplest $a+bi$ form, which is $28 - 96i$ .