Question

let ( z = (4 + 2i) ). which graph represents ( 2z )?

Explanation:

Step1: Calculate 2z

Given $z = 4 + 2i$, multiply by 2:
$2z = 2(4 + 2i) = 8 + 4i$

Step2: Identify coordinate pairs

• $z$ corresponds to the point $(4, 2)$ (real part = 4, imaginary part = 2)
• $2z$ corresponds to the point $(8, 4)$ (real part = 8, imaginary part = 4)

Step3: Match to graph

The correct graph shows $z$ at $(4,2)$ and $2z$ at $(8,4)$, which is the fourth graph (rightmost one).

Answer:

The rightmost graph (with $z$ at (4,2) and $2z$ at (8,4)) represents $2z$.