natics III Sem 2
L 1.8.4 Quiz: Multiplying and Dividing Complex Numbers
Question 4 of 10
Find the quotient of these complex numbers.
\[
(5-i) \div(3+2 i)=
\]
A. $\frac{17}{5}-\frac{13}{5} ;$
B. $\frac{13}{5}-\frac{13}{5}$;
C. $1-i$
D. $\frac{17}{13}-i$

Step 1 ：The question is asking for the quotient of two complex numbers. To find the quotient of two complex numbers, we need to multiply the numerator and the denominator by the conjugate of the denominator. The conjugate of a complex number is obtained by changing the sign of its imaginary part. So, the conjugate of \((3+2i)\) is \((3-2i)\).

Step 2 ：Calculate the numerator by multiplying \((5 - i)\) with the conjugate of the denominator \((3 - 2i)\).

Step 3 ：Calculate the denominator by multiplying \((3 + 2i)\) with its conjugate \((3 - 2i)\).

Step 4 ：Divide the calculated numerator by the calculated denominator to get the quotient.

Step 5 ：Simplify the quotient to get it in the standard form for complex numbers \((a + bi)\).

Step 6 ：Final Answer: The quotient of the complex numbers \((5-i) \div(3+2 i)\) is \(\boxed{1 - i}\).