Question

use the graph to answer the question. by what factor is ( z ) multiplied to get ( z_1 )? answer:

Explanation:

Step1: Identify complex numbers

From the graph:
$z = 3 + 2i$
$z_1 = -6 - 4i$

Step2: Find the scaling factor

Let the factor be $k$. Set up the equation:
$k \cdot z = z_1$
Substitute the values:
$k(3 + 2i) = -6 - 4i$
Solve for $k$:
$k = \frac{-6 - 4i}{3 + 2i} = \frac{-2(3 + 2i)}{3 + 2i} = -2$

Answer:

$-2$