Divide the following complex numbers. (25+19 i)/(5-3i)

Multiply by conjugate: To divide complex numbers, we multiply the numerator and denominator by the conjugate of the denominator. The conjugate of (5-3i) is (5+3i). (25+19i)/(5-3i) * (5+3i)/(5+3i)Multiply numerators and denominators: Now, we multiply the numerators together and the denominators together. Numerator: (25+19i)(5+3i) Denominator: (5-3i)(5+3i)Multiply out the numerator: First, we'll multiply out the numerator using the distributive property (FOIL method). (25+19i)(5+3i) = 25*5 + 25*3i + 19i*5 + 19i*3i = 125 + 75i + 95i + 57i^2 Since i^2 = -1, we replace 57i^2 with -57. = 125 + 75i + 95i - 57 = 125 + 170i - 57 = 68 + 170iMultiply out the denominator: Next, we'll multiply out the denominator. (5-3i)(5+3i) = 5*5 + 5*3i - 3i*5 - 3i*3i = 25 + 15i - 15i - 9i^2 Since i^2 = -1, we replace -9i^2 with 9. = 25 - 9 = 16Simplify numerator and denominator: Now we have the simplified numerator and denominator. Numerator: 68 + 170i Denominator: 16 We divide both the real and imaginary parts of the numerator by the denominator. (68 + 170i) / 16 = 68/16 + (170/16)i = 4.25 + 10.625i

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Divide the following complex numbers.

(25+19 i)/(5-3i)

Divide the following complex numbers. $\newline$ $\frac{25+19 i}{5-3 i}$

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Algebra 2

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Q. Divide the following complex numbers.

\newline

\frac{25+19 i}{5-3 i}

Multiply by conjugate: To divide complex numbers, we multiply the numerator and denominator by the conjugate of the denominator. The conjugate of $(5-3i)$ is $(5+3i)$ . $\frac{25+19i}{5-3i} \times \frac{5+3i}{5+3i}$
Multiply numerators and denominators: Now, we multiply the numerators together and the denominators together. $\newline$ Numerator: $(25+19i)(5+3i)$ $\newline$ Denominator: $(5-3i)(5+3i)$
Multiply out the numerator: First, we'll multiply out the numerator using the distributive property (FOIL method). $\newline$ $(25+19i)(5+3i) = 25\cdot 5 + 25\cdot 3i + 19i\cdot 5 + 19i\cdot 3i$ $\newline$ $= 125 + 75i + 95i + 57i^2$ $\newline$ Since $i^2 = -1$ , we replace $57i^2$ with $-57$ . $\newline$ $= 125 + 75i + 95i - 57$ $\newline$ $= 125 + 170i - 57$ $\newline$ $= 68 + 170i$
Multiply out the denominator: Next, we'll multiply out the denominator. $\newline$ $(5-3i)(5+3i) = 5\times 5 + 5\times 3i - 3i\times 5 - 3i\times 3i$ $\newline$ $= 25 + 15i - 15i - 9i^2$ $\newline$ Since $i^2 = -1$ , we replace $-9i^2$ with $9$ . $\newline$ $= 25 - 9$ $\newline$ $= 16$
Simplify numerator and denominator: Now we have the simplified numerator and denominator. $\newline$ Numerator: $68 + 170i$ $\newline$ Denominator: $16$ $\newline$ We divide both the real and imaginary parts of the numerator by the denominator. $\newline$ $(68 + 170i) / 16$ $\newline$ $= 68/16 + (170/16)i$ $\newline$ $= 4.25 + 10.625i$