Answer the following question. Each positive integer can be written as a sum or difference of distinct integer powers of 3 in only one way. For example, 1 = 3°, 6 = 32 – 31, and 87 = 34 + 32 – 31. Note that 6 = 31 + 31 is not valid since the powers of 3 used are not distinct. Write 2021 as a sum or difference of distinct integer powers of 3. (Remember: Your solution must show appropriate work or reasoning.)

Q: (3-4) (2+31) + 61 can be simplify to

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Q: 2. Find the square roots of the complex number: Z=3+4√7 i

A: Square root of complex number

Q: 7. Multiply the following two complex numbers: (4 - 5i)(-2 + 7i)

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Q: Find the k=8 root of the 10th root of 1+i. Express the answer in rectangular form in 4 decimal…

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Q: Simplify the following con

A: Given,        -13+3i43

Q: (square root of 2-i)6

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Q: Find the three cube roots of 1.

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Q: Two numbers are reciprocals of each other if they have different signs in front. O True O False

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Q: simplify each complex fraction. (3 + 2/(n + 4))/(5 - 1/(n + 4))

A: Solution: Consider the complex fraction: 3+2n+45-1n+4 we have 3 + 2 = 5 5 -1 = 4 Then 3+2n+45-1n+4 =…

Q: If a = (-1,-4, 4) and b =, then a x b equals: O-4i-k O 4i+k O i+ 4k O 4i+k None of the others.

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Q: What is the simplified form of the complex mumber А. 1 C. 8+ 6v3i D.-10-i В.

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Q: 2+Si 6-8i

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Q: Find the 3rd roots of the following complex number: 27cis(174∘) Do not round and type "degree" for…

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Q: QUESTION 3 27a4 863

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Q: The question asks: Simplify the expression, and eliminate any negative exponents. Assume that all…

A: Yes, you are right. We add the exponents because the bases are same.

Q: 1. Write the complex number i+2 in the form of rei® .

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Q: Find the imaginary part of 2 to the power i+3

A: 2i+3 = 23•2i = 8•2i  Now, 2i = ei•ln(2) = cos{ln(2)} + i•sin{ln(2)}

Q: Find the real component if the

A: Given,             a+bi Here,         a=9,  b=10, and n=7.

Q: Find the distinct roots of (-7 + 2i)3/4

A: Let x= (-7 + 2i)3/4 ⇒x4=-7+2i3 On Simplifying, ⇒x4=-259+286i--(1) Let, x=u+iv Now,…

Q: When 3+4i / 2+i is expressed in the form a + bi, what is the value of a?

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Q: (2-6i)+ (6- 5i)

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Q: Find the 5 fifth roots of -4+5i.

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Q: Express in terms of i. - 80 - 80 = (Simplify your answer. Type your answer in the form a+bi.)

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Q: Simplify the following: 3+7i 1. (4 + 2i) + (–3 – 51) 2. (–3 + 4i) – (5+ 2i) in standard form 3.…

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