Express as a complex number in simplest a+bi form: (24+23 i)/(-9+2i) Answer:

Multiply Conjugate: Multiply the numerator and denominator by the conjugate of the denominator to remove the imaginary unit from the denominator. The conjugate of (-9+2i) is (-9-2i). (24+23i)/(-9+2i) * (-9-2i)/(-9-2i)Apply Distributive Property: Apply the distributive property (foil method) to multiply out the numerators and the denominators. Numerator: (24+23i) * (-9-2i) = 24*(-9) + 24*(-2i) + 23i*(-9) + 23i*(-2i) Denominator: (-9+2i) * (-9-2i) = (-9)*(-9) + (-9)*(-2i) + 2i*(-9) + 2i*(-2i)Perform Multiplication: Perform the multiplication for both the numerator and the denominator. Numerator: -216 - 48i - 207i - 46i^2 Since i^2 = -1, replace -46i^2 with 46. Numerator: -216 - 48i - 207i + 46 Denominator: 81 - 18i + 18i - 4i^2 Since i^2 = -1, replace -4i^2 with 4. Denominator: 81 + 4Combine Like Terms: Combine like terms in both the numerator and the denominator. Numerator: (-216 + 46) + (-48i - 207i) = -170 - 255i Denominator: (81 + 4) = 85Divide Complex Numbers: Divide the numerator by the denominator to get the complex number in a+bi form. (-170 - 255i) / 85 = -170/85 - (255i/85)Simplify Fractions: Simplify the fractions. -170/85 = -2 -255i/85 = -3i So, the complex number in a+bi form is -2 - 3i.

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

(24+23 i)/(-9+2i)
Answer:

Express as a complex number in simplest a+bi form: $\newline$ $\frac{24+23 i}{-9+2 i}$ $\newline$ Answer:

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Algebra 2

Write a quadratic function from its x-intercepts and another point

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

\newline

\frac{24+23 i}{-9+2 i}

\newline

Answer:

Multiply Conjugate: Multiply the numerator and denominator by the conjugate of the denominator to remove the imaginary unit from the denominator. $\newline$ The conjugate of $(-9+2i)$ is $(-9-2i)$ . $\newline$ $\frac{24+23i}{-9+2i} \cdot \frac{-9-2i}{-9-2i}$
Apply Distributive Property: Apply the distributive property (foil method) to multiply out the numerators and the denominators. $\newline$ Numerator: $(24+23i) \times (-9-2i) = 24\times(-9) + 24\times(-2i) + 23i\times(-9) + 23i\times(-2i)$ $\newline$ Denominator: $(-9+2i) \times (-9-2i) = (-9)\times(-9) + (-9)\times(-2i) + 2i\times(-9) + 2i\times(-2i)$
Perform Multiplication: Perform the multiplication for both the numerator and the denominator. $\newline$ Numerator: $-216 - 48i - 207i - 46i^2$ $\newline$ Since $i^2 = -1$ , replace $-46i^2$ with $46$ . $\newline$ Numerator: $-216 - 48i - 207i + 46$ $\newline$ Denominator: $81 - 18i + 18i - 4i^2$ $\newline$ Since $i^2 = -1$ , replace $-4i^2$ with $4$ . $\newline$ Denominator: $81 + 4$
Combine Like Terms: Combine like terms in both the numerator and the denominator. $\newline$ Numerator: $(-216 + 46) + (-48i - 207i) = -170 - 255i$ $\newline$ Denominator: $(81 + 4) = 85$
Divide Complex Numbers: Divide the numerator by the denominator to get the complex number in $a+bi$ form. $\newline$ $(-170 - 255i) / 85 = -170/85 - (255i/85)$
Simplify Fractions: Simplify the fractions. $\newline$ $-\frac{170}{85} = -2$ $\newline$ $-\frac{255i}{85} = -3i$ $\newline$ So, the complex number in $a+bi$ form is $-2 - 3i$ .