Simplify the expression to a + bi form: (6-5i)^(2) Answer:

Apply formula: To simplify the expression (6-5i)^(2), we need to apply the formula (a-bi)^2 = a^2 - 2abi + (bi)^2, where a=6 and b=5. Calculation: (6-5i)^2 = 6^2 - 2*6*5i + (5i)^2Calculate real part square: First, we calculate the square of the real part, which is 6^2. Calculation: 6^2 = 36Calculate double product: Next, we calculate the double product of the real part and the imaginary part, which is -2*6*5i. Calculation: -2*6*5i = -60iCalculate imaginary part square: Finally, we calculate the square of the imaginary part, which is (5i)^2. Remember that i^2 = -1. Calculation: (5i)^2 = 25i^2 = 25*(-1) = -25Combine all parts: Now, we combine all the parts together to get the simplified expression. Calculation: 36 - 60i - 25Combine real and imaginary parts: Combine the real parts and the imaginary parts separately. Calculation: (36 - 25) + (-60i) = 11 - 60i

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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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(6-5 i)^{2}

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Answer:

Apply formula: To simplify the expression $(6-5i)^{2}$ , we need to apply the formula $(a-bi)^2 = a^2 - 2abi + (bi)^2$ , where $a=6$ and $b=5$ . Calculation: $(6-5i)^2 = 6^2 - 2\cdot6\cdot5i + (5i)^2$
Calculate real part square: First, we calculate the square of the real part, which is $6^2$ . $\newline$ Calculation: $6^2 = 36$
Calculate double product: Next, we calculate the double product of the real part and the imaginary part, which is $-2 \times 6 \times 5i$ . $\newline$ Calculation: $-2 \times 6 \times 5i = -60i$
Calculate imaginary part square: Finally, we calculate the square of the imaginary part, which is $(5i)^2$ . Remember that $i^2 = -1$ . $\newline$ Calculation: $(5i)^2 = 25i^2 = 25*(-1) = -25$
Combine all parts: Now, we combine all the parts together to get the simplified expression. $\newline$ Calculation: $36 - 60i - 25$
Combine real and imaginary parts: Combine the real parts and the imaginary parts separately. $\newline$ Calculation: $(36 - 25) + (-60i) = 11 - 60i$