Express as a complex number in simplest a+bi form: (12-21 i)/(-6-9i) Answer:

Identify Complex Number: Identify the complex number to be simplified. We have the complex number (12-21i)/(-6-9i) that we need to express in the form a+bi.Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator. The conjugate of the denominator -6-9i is -6+9i. We multiply both the numerator and the denominator by this conjugate to remove the imaginary part from the denominator. ((12-21i)(-6+9i)) / ((-6-9i)(-6+9i))Numerator Multiplication: Perform the multiplication in the numerator. (12-21i)(-6+9i) = 12(-6) + 12(9i) - 21i(-6) - 21i(9i) = -72 + 108i + 126i - 189i^2 Since i^2 = -1, we replace i^2 with -1. = -72 + 108i + 126i + 189 = 117 + 234iDenominator Multiplication: Perform the multiplication in the denominator. (-6-9i)(-6+9i) = (-6)(-6) + (-6)(9i) - 9i(-6) - 9i(9i) = 36 - 54i + 54i - 81i^2 Again, since i^2 = -1, we replace i^2 with -1. = 36 - 54i + 54i + 81 = 117Divide Numerator by Denominator: Divide the results from the numerator by the denominator. (117 + 234i) / 117 We can split this into two fractions, one for the real part and one for the imaginary part. 117/117 + (234i/117) = 1 + 2iFinal Answer: Write the final answer in a+bi form. The simplified form of the complex number is 1 + 2i.

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

(12-21 i)/(-6-9i)
Answer:

Express as a complex number in simplest a+bi form: $\newline$ $\frac{12-21 i}{-6-9 i}$ $\newline$ Answer:

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Algebra 2

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

\newline

\frac{12-21 i}{-6-9 i}

\newline

Answer:

Identify Complex Number: Identify the complex number to be simplified. $\newline$ We have the complex number $(12-21i)/(-6-9i)$ that we need to express in the form $a+bi$ .
Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator. $\newline$ The conjugate of the denominator $-6-9i$ is $-6+9i$ . We multiply both the numerator and the denominator by this conjugate to remove the imaginary part from the denominator. $\newline$ $\frac{(12-21i)(-6+9i)}{(-6-9i)(-6+9i)}$
Numerator Multiplication: Perform the multiplication in the numerator. $\newline$ $(12-21i)(-6+9i) = 12(-6) + 12(9i) - 21i(-6) - 21i(9i)$ $\newline$ $= -72 + 108i + 126i - 189i^2$ $\newline$ Since $i^2 = -1$ , we replace $i^2$ with $-1$ . $\newline$ $= -72 + 108i + 126i + 189$ $\newline$ $= 117 + 234i$
Denominator Multiplication: Perform the multiplication in the denominator. $\newline$ $(-6-9i)(-6+9i) = (-6)(-6) + (-6)(9i) - 9i(-6) - 9i(9i)$ $\newline$ $= 36 - 54i + 54i - 81i^2$ $\newline$ Again, since $i^2 = -1$ , we replace $i^2$ with $-1$ . $\newline$ $= 36 - 54i + 54i + 81$ $\newline$ $= 117$
Divide Numerator by Denominator: Divide the results from the numerator by the denominator. $\newline$ $(117 + 234i) / 117$ $\newline$ We can split this into two fractions, one for the real part and one for the imaginary part. $\newline$ $117/117 + (234i/117)$ $\newline$ = $1 + 2i$
Final Answer: Write the final answer in $a+bi$ form. $\newline$ The simplified form of the complex number is $1 + 2i$ .