Express as a complex number in simplest a+bi form: (9+21 i)/(2-5i) 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 (2-5i) is (2+5i). (9+21i)/(2-5i) * (2+5i)/(2+5i)Apply Distributive Property: Apply the distributive property (FOIL method) to multiply out the numerators and denominators. Numerator: (9+21i)(2+5i) = 9*2 + 9*5i + 21i*2 + 21i*5i Denominator: (2-5i)(2+5i) = 2*2 + 2*5i - 5i*2 - 5i*5iPerform Multiplication: Perform the multiplication for both the numerator and the denominator. Numerator: 18 + 45i + 42i + 105i^2 Since i^2 = -1, replace 105i^2 with -105. Numerator becomes: 18 + 45i + 42i - 105 Denominator: 4 + 10i - 10i - 25i^2 Since i^2 = -1, replace -25i^2 with 25. Denominator becomes: 4 + 10i - 10i + 25Simplify Numerator and Denominator: Simplify the numerator and the denominator by combining like terms. Numerator: (18 - 105) + (45i + 42i) = -87 + 87i Denominator: (4 + 25) + (10i - 10i) = 29Divide Numerator by Denominator: Divide the simplified numerator by the simplified denominator. (-87 + 87i) / 29Divide Each Term: Divide each term in the numerator by the denominator separately. -87 / 29 + (87i / 29)Perform Division: Perform the division for each term. -87 / 29 = -3 87i / 29 = 3iWrite Final Answer: Write the final answer in a+bi form. -3 + 3i

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

(9+21 i)/(2-5i)
Answer:

Express as a complex number in simplest a+bi form: $\newline$ $\frac{9+21 i}{2-5 i}$ $\newline$ 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{9+21 i}{2-5 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 $(2-5i)$ is $(2+5i)$ . $\newline$ $\frac{9+21i}{2-5i} \times \frac{2+5i}{2+5i}$
Apply Distributive Property: Apply the distributive property (FOIL method) to multiply out the numerators and denominators. $\newline$ Numerator: $(9+21i)(2+5i) = 9\cdot 2 + 9\cdot 5i + 21i\cdot 2 + 21i\cdot 5i$ $\newline$ Denominator: $(2-5i)(2+5i) = 2\cdot 2 + 2\cdot 5i - 5i\cdot 2 - 5i\cdot 5i$
Perform Multiplication: Perform the multiplication for both the numerator and the denominator. $\newline$ Numerator: $18 + 45i + 42i + 105i^2$ $\newline$ Since $i^2 = -1$ , replace $105i^2$ with $-105$ . $\newline$ Numerator becomes: $18 + 45i + 42i - 105$ $\newline$ Denominator: $4 + 10i - 10i - 25i^2$ $\newline$ Since $i^2 = -1$ , replace $-25i^2$ with $25$ . $\newline$ Denominator becomes: $4 + 10i - 10i + 25$
Simplify Numerator and Denominator: Simplify the numerator and the denominator by combining like terms. $\newline$ Numerator: $(18 - 105) + (45i + 42i) = -87 + 87i$ $\newline$ Denominator: $(4 + 25) + (10i - 10i) = 29$
Divide Numerator by Denominator: Divide the simplified numerator by the simplified denominator. $(-87 + 87i) / 29$
Divide Each Term: Divide each term in the numerator by the denominator separately. $-\frac{87}{29} + \left(\frac{87i}{29}\right)$
Perform Division: Perform the division for each term. $\newline$ $-87 / 29 = -3$ $\newline$ $87i / 29 = 3i$
Write Final Answer: Write the final answer in $a+bi$ form. $\newline$ $-3 + 3i$