Express as a complex number in simplest a+bi form: (24-13 i)/(2+i) Answer:

Multiply by Conjugate: Multiply the numerator and denominator by the conjugate of the denominator to remove the imaginary unit from the denominator. The conjugate of 2+i is 2-i. So, we multiply (24-13i)/(2+i) by (2-i)/(2-i) to rationalize the denominator.Numerator Multiplication: Perform the multiplication in the numerator. Multiply (24-13i) by (2-i). Using the distributive property (FOIL method): 24*2 + 24*(-i) - 13i*2 - 13i*(-i) = 48 - 24i - 26i + 13i^2 Since i^2 = -1, replace 13i^2 with -13. = 48 - 24i - 26i - 13 = 48 - 13 - (24i + 26i) = 35 - 50iDenominator Multiplication: Perform the multiplication in the denominator. Multiply (2+i) by (2-i). Using the difference of squares: 2*2 - i*2 + i*2 - i^2 = 4 - i^2 Since i^2 = -1, replace -i^2 with 1. = 4 + 1 = 5Final Complex Number: Divide the results from Step 2 by the result from Step 3 to get the complex number in a+bi form. f(x) = (35 - 50i) / 5 Divide both the real part and the imaginary part by 5. = 35/5 - (50i/5) = 7 - 10i

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Express as a complex number in simplest a+bi form:

(24-13 i)/(2+i)
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Express as a complex number in simplest a+bi form: $\newline$ $\frac{24-13 i}{2+i}$ $\newline$ Answer:

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Algebra 2

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Q. Express as a complex number in simplest a+bi form:

\newline

\frac{24-13 i}{2+i}

\newline

Answer:

Multiply by Conjugate: Multiply the numerator and denominator by the conjugate of the denominator to remove the imaginary unit from the denominator. $\newline$ The conjugate of $2+i$ is $2-i$ . $\newline$ So, we multiply $(24-13i)/(2+i)$ by $(2-i)/(2-i)$ to rationalize the denominator.
Numerator Multiplication: Perform the multiplication in the numerator. $\newline$ Multiply $(24-13i)$ by $(2-i)$ . $\newline$ Using the distributive property (FOIL method): $\newline$ $24\cdot 2 + 24\cdot (-i) - 13i\cdot 2 - 13i\cdot (-i)$ $\newline$ = $48 - 24i - 26i + 13i^2$ $\newline$ Since $i^2 = -1$ , replace $13i^2$ with $-13$ . $\newline$ = $48 - 24i - 26i - 13$ $\newline$ = $48 - 13 - (24i + 26i)$ $\newline$ = $35 - 50i$
Denominator Multiplication: Perform the multiplication in the denominator. $\newline$ Multiply $(2+i)$ by $(2-i)$ . $\newline$ Using the difference of squares: $\newline$ $2\times 2 - i\times 2 + i\times 2 - i^2$ $\newline$ $= 4 - i^2$ $\newline$ Since $i^2 = -1$ , replace $-i^2$ with $1$ . $\newline$ $= 4 + 1$ $\newline$ $= 5$
Final Complex Number: Divide the results from Step $2$ by the result from Step $3$ to get the complex number in $a+bi$ form. $\newline$ $f(x) = \frac{35 - 50i}{5}$ $\newline$ Divide both the real part and the imaginary part by $5$ . $\newline$ $= \frac{35}{5} - \frac{50i}{5}$ $\newline$ $= 7 - 10i$