Express as a complex number in simplest a+bi form: (-7+9i)/(-5-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 (-5-i) is (-5+i). (-7+9i)/(-5-i) * (-5+i)/(-5+i)Apply Distributive Property: Apply the distributive property (foil method) to both the numerator and the denominator. Numerator: (-7+9i)(-5+i) = 35 - 7i - 45i + 9i^2 Denominator: (-5-i)(-5+i) = 25 - 5i + 5i - i^2Simplify Expressions: Simplify the expressions, remembering that i^2 = -1. Numerator: 35 - 7i - 45i - 9 = 26 - 52i Denominator: 25 + 1 = 26Divide Numerator by Denominator: Divide the simplified numerator by the simplified denominator. (26 - 52i) / 26Split Real and Imaginary Parts: Simplify the division by splitting into real and imaginary parts. 26/26 - (52i/26) 1 - 2i

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

(-7+9i)/(-5-i)
Answer:

Express as a complex number in simplest a+bi form: $\newline$ $\frac{-7+9 i}{-5-i}$ $\newline$ 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{-7+9 i}{-5-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 $(-5-i)$ is $(-5+i)$ . $\newline$ $\frac{-7+9i}{-5-i} \cdot \frac{-5+i}{-5+i}$
Apply Distributive Property: Apply the distributive property (foil method) to both the numerator and the denominator. $\newline$ Numerator: $(-7+9i)(-5+i) = 35 - 7i - 45i + 9i^2$ $\newline$ Denominator: $(-5-i)(-5+i) = 25 - 5i + 5i - i^2$
Simplify Expressions: Simplify the expressions, remembering that $i^2 = -1$ . $\newline$ Numerator: $35 - 7i - 45i - 9 = 26 - 52i$ $\newline$ Denominator: $25 + 1 = 26$
Divide Numerator by Denominator: Divide the simplified numerator by the simplified denominator. $(26 - 52i) / 26$
Split Real and Imaginary Parts: Simplify the division by splitting into real and imaginary parts. $\newline$ $\frac{26}{26} - \frac{52i}{26}$ $\newline$ $1 - 2i$