Simplify: 2(1+3i)-(2-4i)+(5-2i) (A) 5+4i (B) 13 (C) 9+6i (D) 5+8i

Question prompt: Question prompt: Simplify the complex number expression 2(1+3i)-(2-4i)+(5-2i).Distribute and combine: First, distribute the 2 into the first set of parentheses: 2 * 1 + 2 * 3i = 2 + 6i.Combine real parts: Combine the distributed result with the other terms: (2 + 6i) - (2 - 4i) + (5 - 2i).Combine imaginary parts: Now, simplify by combining like terms. First, combine the real parts: 2 - 2 + 5 = 5.Final simplified form: Next, combine the imaginary parts: 6i + 4i - 2i = 8i.Question prompt: Combine the real and imaginary parts to get the final simplified form: 5 + 8i.Recognize sqrt(-81): Question prompt: Simplify the expression (-9+sqrt(-81))/(3).Calculate sqrt(81): Recognize that sqrt(-81) is the square root of a negative number, which can be expressed as sqrt(81) * i, since i is the imaginary unit where i^2 = -1.Substitute in expression: Calculate the square root of 81, which is 9. So, sqrt(-81) = 9i.Divide by 3: Substitute 9i for sqrt(-81) in the expression: (-9+9i)/(3).Simplify terms: Divide both terms in the numerator by 3: (-9/3) + (9i/3).Simplify each term: -3 + 3i.

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Simplify:
2(1+3i)-(2-4i)+(5-2i)
(A) 5+4i
(B) 13
(C) 9+6i
(D) 5+8i

Simplify: $\newline$ $2(1+3 i)-(2-4 i)+(5-2 i)$ $\newline$ (A) $5+4 i$ $\newline$ (B) $13$ $\newline$ (C) $9+6 i$ $\newline$ (D) $5+8 i$

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Q. Simplify:

\newline

2(1+3 i)-(2-4 i)+(5-2 i)

\newline

(A)

5+4 i

\newline

(B)

13

\newline

(C)

9+6 i

\newline

(D)

5+8 i

Question prompt: Question prompt: Simplify the complex number expression $2(1+3i)-(2-4i)+(5-2i)$ .
Distribute and combine: First, distribute the $2$ into the first set of parentheses: $2 \times 1 + 2 \times 3i = 2 + 6i$ .
Combine real parts: Combine the distributed result with the other terms: $(2 + 6i) - (2 - 4i) + (5 - 2i)$ .
Combine imaginary parts: Now, simplify by combining like terms. First, combine the real parts: $2 - 2 + 5 = 5$ .
Final simplified form: Next, combine the imaginary parts: $6i + 4i - 2i = 8i$ .
Question prompt: Combine the real and imaginary parts to get the final simplified form: $5 + 8i$ .
Recognize $\sqrt{-81}$ : Question prompt: Simplify the expression $\frac{-9+\sqrt{-81}}{3}$ .
Calculate $\sqrt{81}$ : Recognize that $\sqrt{-81}$ is the square root of a negative number, which can be expressed as $\sqrt{81} \cdot i$ , since $i$ is the imaginary unit where $i^2 = -1$ .
Substitute in expression: Calculate the square root of $81$ , which is $9$ . So, $\sqrt{-81} = 9i$ .
Divide by $3$ : Substitute $9i$ for $\sqrt{-81}$ in the expression: $(-9+9i)/(3)$ .
Simplify terms: Divide both terms in the numerator by $3$ : $(-9/3) + (9i/3)$ .
Simplify terms: Divide both terms in the numerator by $3$ : $(-9/3) + (9i/3)$ .Simplify each term: $-3 + 3i$ .