Divide the following complex numbers. (-3+15 i)/(3-2i)

Multiply Numerators and Denominators: Now we multiply the numerators and the denominators separately. Numerator: (-3+15i)(3+2i) Denominator: (3-2i)(3+2i)Expand and Combine Numerator: First, we'll expand the numerator using the distributive property (FOIL method). (-3)(3) + (-3)(2i) + (15i)(3) + (15i)(2i) = -9 - 6i + 45i + 30i^2 Since i^2 = -1, we replace 30i^2 with -30. = -9 - 6i + 45i - 30Expand and Combine Denominator: Now we combine like terms in the numerator. -9 - 30 - 6i + 45i = -39 + 39iSimplify Numerator and Denominator: Next, we'll expand the denominator using the distributive property. (3)(3) + (3)(2i) - (2i)(3) - (2i)(2i) = 9 + 6i - 6i - 4i^2 Again, since i^2 = -1, we replace -4i^2 with 4. = 9 + 6i - 6i + 4Divide Numerator by Denominator: Now we combine like terms in the denominator. 9 + 4 + 6i - 6i = 13Final Simplified Form: We now have the simplified numerator and denominator. Numerator: -39 + 39i Denominator: 13 We divide each term in the numerator by the denominator. (-39/13) + (39i/13)Simplify each term. -39/13 = -3 39i/13 = 3i So the final simplified form is: -3 + 3i

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Divide the following complex numbers.

(-3+15 i)/(3-2i)

Divide the following complex numbers. $\newline$ $\frac{-3+15 i}{3-2 i}$

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Algebra 2

Add, subtract, multiply, and divide polynomials

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Q. Divide the following complex numbers.

\newline

\frac{-3+15 i}{3-2 i}

Multiply Numerators and Denominators: Now we multiply the numerators and the denominators separately. $\newline$ Numerator: $(-3+15i)(3+2i)$ $\newline$ Denominator: $(3-2i)(3+2i)$
Expand and Combine Numerator: First, we'll expand the numerator using the distributive property (FOIL method). $\newline$ $(-3)(3) + (-3)(2i) + (15i)(3) + (15i)(2i)$ $\newline$ = $-9 - 6i + 45i + 30i^2$ $\newline$ Since $i^2 = -1$ , we replace $30i^2$ with $-30$ . $\newline$ = $-9 - 6i + 45i - 30$
Expand and Combine Denominator: Now we combine like terms in the numerator. $\newline$ $-9 - 30 - 6i + 45i$ $\newline$ $= -39 + 39i$
Simplify Numerator and Denominator: Next, we'll expand the denominator using the distributive property. $\newline$ $(3)(3) + (3)(2i) - (2i)(3) - (2i)(2i)$ $\newline$ $= 9 + 6i - 6i - 4i^2$ $\newline$ Again, since $i^2 = -1$ , we replace $-4i^2$ with $4$ . $\newline$ $= 9 + 6i - 6i + 4$
Divide Numerator by Denominator: Now we combine like terms in the denominator. $\newline$ $9 + 4 + 6i - 6i$ $\newline$ = $13$
Final Simplified Form: We now have the simplified numerator and denominator. $\newline$ Numerator: $-39 + 39i$ $\newline$ Denominator: $13$ $\newline$ We divide each term in the numerator by the denominator. $\newline$ $(-39/13) + (39i/13)$
Final Simplified Form: We now have the simplified numerator and denominator. $\newline$ Numerator: $-39 + 39i$ $\newline$ Denominator: $13$ $\newline$ We divide each term in the numerator by the denominator. $\newline$ $(-39/13) + (39i/13)$ Simplify each term. $\newline$ $-39/13 = -3$ $\newline$ $39i/13 = 3i$ $\newline$ So the final simplified form is: $\newline$ $-3 + 3i$