Question

review the four points on the complex plane. which point represents the quotient of \\(\frac{4 + 3i}{-i}\\)? (options: a, b, c, d. and there is a complex plane graph with points b, a, c, d marked.)

Explanation:

Step1: Rationalize the denominator

Multiply numerator and denominator by $i$ (since $-i \times i = 1$):
$\frac{(4+3i) \times i}{-i \times i}$

Step2: Expand numerator and simplify denominator

Calculate products:
$\frac{4i + 3i^2}{-i^2}$
Substitute $i^2=-1$:
$\frac{4i + 3(-1)}{-(-1)} = \frac{-3 + 4i}{1} = -3 + 4i$

Step3: Locate the complex number

A complex number $a+bi$ corresponds to $(a,b)$ on the complex plane. For $-3+4i$, this is the point $(-3,4)$, which is point B.

Answer:

B. Point B (corresponding to $-3 + 4i$)