Express as a complex number in simplest a+bi form: (-2+5i)/(-1+i) Answer:

Multiply by Conjugate: Multiply the numerator and denominator by the conjugate of the denominator to eliminate the imaginary unit i from the denominator. The conjugate of (-1+i) is (-1-i). (-2+5i)/(-1+i) * (-1-i)/(-1-i)Apply Distributive Property: Apply the distributive property (foil method) to multiply out the numerators and denominators. Numerator: (-2+5i) * (-1-i) = (-2)(-1) + (-2)(-i) + (5i)(-1) + (5i)(-i) Denominator: (-1+i) * (-1-i) = (-1)(-1) + (-1)(-i) + (i)(-1) + (i)(-i)Perform Multiplication: Perform the multiplication for both the numerator and the denominator. Numerator: 2 + 2i - 5i - 5i^2 Since i^2 = -1, replace i^2 with -1. Numerator: 2 + 2i - 5i + 5 Denominator: 1 - i + i - i^2 Similarly, replace i^2 with -1 in the denominator. Denominator: 1 + 1Combine Like Terms: Combine like terms in both the numerator and the denominator. Numerator: (2 + 5) + (2i - 5i) Numerator: 7 - 3i Denominator: 1 + 1 Denominator: 2Divide to Get Complex Number: Divide the numerator by the denominator to get the complex number in a+bi form. (7 - 3i) / 2 a = 7/2 b = -3/2 So the complex number in a+bi form is 7/2 - 3/2i.

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

(-2+5i)/(-1+i)
Answer:

Express as a complex number in simplest a+bi form: $\newline$ $\frac{-2+5 i}{-1+i}$ $\newline$ 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{-2+5 i}{-1+i}

\newline

Answer:

Multiply by Conjugate: Multiply the numerator and denominator by the conjugate of the denominator to eliminate the imaginary unit $i$ from the denominator. $\newline$ The conjugate of $(-1+i)$ is $(-1-i)$ . $\newline$ $\frac{-2+5i}{-1+i} \cdot \frac{-1-i}{-1-i}$
Apply Distributive Property: Apply the distributive property (foil method) to multiply out the numerators and denominators. $\newline$ Numerator: $(-2+5i) \times (-1-i) = (-2)(-1) + (-2)(-i) + (5i)(-1) + (5i)(-i)$ $\newline$ Denominator: $(-1+i) \times (-1-i) = (-1)(-1) + (-1)(-i) + (i)(-1) + (i)(-i)$
Perform Multiplication: Perform the multiplication for both the numerator and the denominator. $\newline$ Numerator: $2 + 2i - 5i - 5i^2$ $\newline$ Since $i^2 = -1$ , replace $i^2$ with $-1$ . $\newline$ Numerator: $2 + 2i - 5i + 5$ $\newline$ Denominator: $1 - i + i - i^2$ $\newline$ Similarly, replace $i^2$ with $-1$ in the denominator. $\newline$ Denominator: $1 + 1$
Combine Like Terms: Combine like terms in both the numerator and the denominator. $\newline$ Numerator: $(2 + 5) + (2i - 5i)$ $\newline$ Numerator: $7 - 3i$ $\newline$ Denominator: $1 + 1$ $\newline$ Denominator: $2$
Divide to Get Complex Number: Divide the numerator by the denominator to get the complex number in $a+bi$ form. $\newline$ $(7 - 3i) / 2$ $\newline$ $a = \frac{7}{2}$ $\newline$ $b = -\frac{3}{2}$ $\newline$ So the complex number in $a+bi$ form is $\frac{7}{2} - \frac{3}{2}i$ .