Express as a complex number in simplest a+bi form: (-2+9i)/(-3-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 (-3-i) is (-3+i). (-2+9i)/(-3-i) * (-3+i)/(-3+i)Apply distributive property: Apply the distributive property (FOIL method) to both the numerator and the denominator. Numerator: (-2+9i)(-3+i) = (-2)(-3) + (-2)(i) + (9i)(-3) + (9i)(i) Denominator: (-3-i)(-3+i) = (-3)(-3) + (-3)(i) + (-i)(-3) + (-i)(i)Perform multiplication: Perform the multiplication for both the numerator and the denominator. Numerator: 6 - 2i - 27i - 9i^2 Since i^2 = -1, we have -9i^2 = 9. Numerator becomes: 6 - 2i - 27i + 9 Denominator: 9 - 3i + 3i - i^2 Since i^2 = -1, we have -i^2 = 1. Denominator becomes: 9 + 1Combine like terms: Combine like terms in both the numerator and the denominator. Numerator: (6 + 9) - (2i + 27i) = 15 - 29i Denominator: 9 + 1 = 10Write in a+bi form: Write the complex number in a+bi form by dividing the real and imaginary parts by the denominator. Real part: 15/10 = 1.5 Imaginary part: -29i/10 = -2.9i So, the complex number in a+bi form is 1.5 - 2.9i.

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

(-2+9i)/(-3-i)
Answer:

Express as a complex number in simplest a+bi form: $\newline$ $\frac{-2+9 i}{-3-i}$ $\newline$ Answer:

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Algebra 2

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

\newline

\frac{-2+9 i}{-3-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 $(-3-i)$ is $(-3+i)$ . $\newline$ $\frac{-2+9i}{-3-i} \times \frac{-3+i}{-3+i}$
Apply distributive property: Apply the distributive property (FOIL method) to both the numerator and the denominator. $\newline$ Numerator: $(-2+9i)(-3+i) = (-2)(-3) + (-2)(i) + (9i)(-3) + (9i)(i)$ $\newline$ Denominator: $(-3-i)(-3+i) = (-3)(-3) + (-3)(i) + (-i)(-3) + (-i)(i)$
Perform multiplication: Perform the multiplication for both the numerator and the denominator. $\newline$ Numerator: $6 - 2i - 27i - 9i^2$ $\newline$ Since $i^2 = -1$ , we have $-9i^2 = 9$ . $\newline$ Numerator becomes: $6 - 2i - 27i + 9$ $\newline$ Denominator: $9 - 3i + 3i - i^2$ $\newline$ Since $i^2 = -1$ , we have $-i^2 = 1$ . $\newline$ Denominator becomes: $9 + 1$
Combine like terms: Combine like terms in both the numerator and the denominator. $\newline$ Numerator: $(6 + 9) - (2i + 27i) = 15 - 29i$ $\newline$ Denominator: $9 + 1 = 10$
Write in $a+bi$ form: Write the complex number in $a+bi$ form by dividing the real and imaginary parts by the denominator. $\newline$ Real part: $\frac{15}{10} = 1.5$ $\newline$ Imaginary part: $\frac{-29i}{10} = -2.9i$ $\newline$ So, the complex number in $a+bi$ form is $1.5 - 2.9i$ .