Question

review the graph.
given ( z_1 = 5 - 2i ) and ( z_2 = 3 + 2i ), which letter represents ( z_1 - z_2 )?
a
b
c
d

Explanation:

Step1: Subtract the complex numbers

To find \( z_1 - z_2 \), we subtract the real parts and the imaginary parts separately. Given \( z_1 = 5 - 2i \) and \( z_2 = 3 + 2i \), we have:
\[

$$\begin{align*} z_1 - z_2&=(5 - 2i)-(3 + 2i)\\ &=5 - 2i - 3 - 2i\\ &=(5 - 3)+(-2i - 2i)\\ &=2 - 4i \end{align*}$$

\]

Step2: Identify the point on the graph

A complex number \( a + bi \) is represented as the point \( (a, b) \) on the complex plane (where the x - axis is the real axis and the y - axis is the imaginary axis). For \( 2 - 4i \), the real part \( a = 2 \) and the imaginary part \( b=-4 \). So the point is \( (2,-4) \). Looking at the graph, point A has coordinates that match \( (2, - 4) \) (assuming the grid is such that we can identify the position of A as having a real part of 2 and an imaginary part of - 4).

Answer:

A