# How do you find the power #(3-6i)^4# and express the result in rectangular form?

I would just square twice in rectangular form:

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To find the power ((3-6i)^4) and express the result in rectangular form:

- Expand ((3-6i)^4) using the binomial theorem or by successive multiplication.
- Combine like terms and express the result in the form (a + bi), where (a) and (b) are real numbers.

Let's go through the steps:

[ \begin{align*} (3-6i)^4 & = (3-6i)(3-6i)(3-6i)(3-6i) \ & = (3-6i)(3-6i)((3-6i)(3-6i)) \ & = (3-6i)(3-6i)(9-36i-36i+36) \ & = (3-6i)(3-6i)(9-72i+36) \ & = (3-6i)(3-6i)(45-72i) \ & = (3 \cdot 3 - 3 \cdot 6i - 6i \cdot 3 + 6i \cdot 6i)(45-72i) \ & = (9 - 18i - 18i + 36i^2)(45-72i) \ & = (9 - 36i - 36i - 36)(45-72i) \ & = (-27 - 72i)(45-72i) \ & = -27(45) - 27(-72i) - 72i(45) - 72i(-72i) \ & = -1215 + 1944i - 3240i - 5184 \ & = -1215 - 1296 - 1296i \ & = -351 - 1296i \end{align*} ]

Therefore, ((3-6i)^4 = -351 - 1296i) in rectangular form.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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