Simplify the expression to a + bi form: (11+8i)^(2) Answer:

Expand Expression: Expand the expression using the formula (a + bi)^2 = a^2 + 2abi - b^2, where a = 11 and b = 8. Calculation: (11 + 8i)^2 = 11^2 + 2*11*8i + (8i)^2Calculate Real Part Square: Calculate the square of the real part, which is 11^2. Calculation: 11^2 = 121Calculate Real-Imaginary Product: Calculate the product of the real part and the imaginary part, multiplied by 2, which is 2*11*8i. Calculation: 2*11*8i = 176iCalculate Imaginary Part Square: Calculate the square of the imaginary part, which is (8i)^2. Calculation: (8i)^2 = 64i^2 Since i^2 = -1, we have 64i^2 = 64*(-1) = -64Combine Results: Combine the results from steps 2, 3, and 4 to get the final expression in a + bi form. Calculation: 121 + 176i - 64Simplify Expression: Simplify the expression by combining the real parts and keeping the imaginary part as is. Calculation: (121 - 64) + 176i = 57 + 176i

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Q. Simplify the expression to a + bi form:

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(11+8 i)^{2}

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Answer:

Expand Expression: Expand the expression using the formula $(a + bi)^2 = a^2 + 2abi - b^2$ , where $a = 11$ and $b = 8$ . $\newline$ Calculation: $(11 + 8i)^2 = 11^2 + 2\cdot11\cdot8i + (8i)^2$
Calculate Real Part Square: Calculate the square of the real part, which is $11^2$ . $\newline$ Calculation: $11^2 = 121$
Calculate Real-Imaginary Product: Calculate the product of the real part and the imaginary part, multiplied by $2$ , which is $2\times 11\times 8i$ . $\newline$ Calculation: $2\times 11\times 8i = 176i$
Calculate Imaginary Part Square: Calculate the square of the imaginary part, which is $(8i)^2$ . $\newline$ Calculation: $(8i)^2 = 64i^2$ $\newline$ Since $i^2 = -1$ , we have $64i^2 = 64*(-1) = -64$
Combine Results: Combine the results from steps $2$ , $3$ , and $4$ to get the final expression in $a + bi$ form. $\newline$ Calculation: $121 + 176i - 64$
Simplify Expression: Simplify the expression by combining the real parts and keeping the imaginary part as is. $\newline$ Calculation: $(121 - 64) + 176i = 57 + 176i$