Simplify the expression to a + bi form: (-3-i)^(2) Answer:

Write Expression: Write down the expression to be simplified. We need to square the complex number (-3 - i). (-3 - i)^(2)Apply Formula: Apply the formula (a - b)^2 = a^2 - 2ab + b^2 to the complex number, where a = -3 and b = i. (-3 - i)^2 = (-3)^2 - 2(-3)(i) + (i)^2Calculate Terms: Calculate each term separately. (-3)^2 = 9 2(-3)(i) = -6i (i)^2 = -1 (since i^2 = -1)Substitute Values: Substitute the calculated values back into the expression. (-3 - i)^2 = 9 - (-6i) - 1Simplify Expression: Simplify the expression by combining like terms. 9 - (-6i) - 1 = 9 + 6i - 1Combine Real and Imaginary Parts: Combine the real parts and the imaginary parts. 9 + 6i - 1 = (9 - 1) + 6i 8 + 6i

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Algebra 2

Simplify variable expressions using properties

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Q. Simplify the expression to a + bi form:

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(-3-i)^{2}

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Answer:

Write Expression: Write down the expression to be simplified. $\newline$ We need to square the complex number $(-3 - i)$ . $\newline$ $(-3 - i)^{2}$
Apply Formula: Apply the formula $(a - b)^2 = a^2 - 2ab + b^2$ to the complex number, where $a = -3$ and $b = i$ . $(-3 - i)^2 = (-3)^2 - 2(-3)(i) + (i)^2$
Calculate Terms: Calculate each term separately. $\newline$ $(-3)^2 = 9$ $\newline$ $2(-3)(i) = -6i$ $\newline$ $(i)^2 = -1$ (since $i^2 = -1$ )
Substitute Values: Substitute the calculated values back into the expression. $(-3 - i)^2 = 9 - (-6i) - 1$
Simplify Expression: Simplify the expression by combining like terms. $9 - (-6i) - 1 = 9 + 6i - 1$
Combine Real and Imaginary Parts: Combine the real parts and the imaginary parts. $\newline$ $9 + 6i - 1 = (9 - 1) + 6i$ $\newline$ $8 + 6i$