Simplify the expression to a + bi form: (-9+2i)^(2) Answer:

Square Real Part: To simplify the expression (-9+2i)^(2), we need to square the complex number (-9+2i). This involves using the formula (a+bi)^2 = a^2 + 2abi - b^2, where a = -9 and b = 2.Multiply Real and Imaginary: First, we square the real part a, which is -9. So, (-9)^2 = 81.Square Imaginary Part: Next, we multiply the real part a by the imaginary part b by 2. So, 2 * (-9) * 2i = -36i.Combine All Parts: Then, we square the imaginary part b, which is 2i. So, (2i)^2 = 4i^2. Since i^2 = -1, this simplifies to 4 * (-1) = -4.Simplify Expression: Now, we combine all the parts together: 81 (from the real part squared) + (-36i) (from the double product of a and b) - 4 (from the imaginary part squared).Simplifying the expression, we get 81 - 4 - 36i, which is 77 - 36i.

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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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(-9+2 i)^{2}

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Answer:

Square Real Part: To simplify the expression $(-9+2i)^{2}$ , we need to square the complex number $(-9+2i)$ . This involves using the formula $(a+bi)^2 = a^2 + 2abi - b^2$ , where $a = -9$ and $b = 2$ .
Multiply Real and Imaginary: First, we square the real part $a$ , which is $-9$ . So, $(-9)^2 = 81$ .
Square Imaginary Part: Next, we multiply the real part $a$ by the imaginary part $b$ by $2$ . So, $2 \times (-9) \times 2i = -36i$ .
Combine All Parts: Then, we square the imaginary part $b$ , which is $2i$ . So, $(2i)^2 = 4i^2$ . Since $i^2 = -1$ , this simplifies to $4 \times (-1) = -4$ .
Simplify Expression: Now, we combine all the parts together: $81$ (from the real part squared) + $(-36i)$ (from the double product of $a$ and $b$ ) - $4$ (from the imaginary part squared).
Simplify Expression: Now, we combine all the parts together: $81$ (from the real part squared) + $(-36i)$ (from the double product of $a$ and $b$ ) - $4$ (from the imaginary part squared).Simplifying the expression, we get $81 - 4 - 36i$ , which is $77 - 36i$ .