Question

review the graph. suppose ( z_1 = 7 - 3i ) and ( z_2 = 3 - 5i ). which letter represents the sum ( z_1 + z_2 )?
a
b
c
d

Explanation:

Step1: Add real parts

To find \( z_1 + z_2 \), first add the real parts of \( z_1 = 7 - 3i \) and \( z_2 = 3 - 5i \). The real parts are \( 7 \) and \( 3 \). So, \( 7 + 3 = 10 \).

Step2: Add imaginary parts

The imaginary parts are \( -3i \) and \( -5i \). So, \( -3i + (-5i) = -8i \).

Step3: Determine the complex number

Combining the real and imaginary parts, we get \( z_1 + z_2 = 10 - 8i \). On the complex plane, the real part is the x - coordinate and the imaginary part (coefficient of \( i \)) is the y - coordinate. So the point representing \( 10 - 8i \) has real part \( 10 \) and imaginary part \( -8 \). Looking at the graph, point C has real part around 10 and imaginary part - 8 (since it's below the real axis, negative imaginary part).

Answer:

C