Which of the following complex numbers is equivalent to (3-5 i)/(8+2 i) ?( Note: i=√(-1)) A

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Which of the following complex numbers is equivalent to (3-5...

Which of the following complex numbers is equivalent to $\frac{3-5 i}{8+2 i} ?($ Note: $i=\sqrt{-1})$ \begin{equation} \begin{array}{l}{\text { A) } \frac{3}{8}-\frac{5 i}{2}} \\ {\text { B) } \frac{3}{8}+\frac{5 i}{2}} \\ {\text { C) } \frac{7}{34}-\frac{23 i}{34}} \\ {\text { D) } \frac{7}{34}+\frac{23 i}{34}}\end{array} \end{equation}

Which of the following complex numbers is
equivalent to $\frac{3-5 i}{8+2 i} ?($ Note: $i=\sqrt{-1})$
\begin{equation}
\begin{array}{l}{\text { A) } \frac{3}{8}-\frac{5 i}{2}} \\ {\text { B) } \frac{3}{8}+\frac{5 i}{2}} \\ {\text { C) } \frac{7}{34}-\frac{23 i}{34}} \\ {\text { D) } \frac{7}{34}+\frac{23 i}{34}}\end{array}
\end{equation}

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Key Concepts

Simplification of Complex Rational Expressions

Simplifying complex rational expressions involves using the conjugate to remove the imaginary unit from the denominator, allowing the expression to be rewritten clearly as a sum of a real part and an imaginary part.

Conjugate of a Complex Number

The conjugate of a complex number a + bi is a - bi. Multiplying a complex number by its conjugate results in a real number, which is crucial for simplifying expressions where the denominator is complex.

Complex Numbers

Complex numbers are numbers that have both a real and an imaginary component, typically expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit satisfying i² = -1.

Division of Complex Numbers

Dividing complex numbers involves expressing the division in a form that separates real and imaginary parts. This is achieved by multiplying both the numerator and the denominator by the conjugate of the denominator to eliminate the imaginary part from the denominator.

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