Question

A collection of points is shown on the complex plane. points on the complex plane, point z sub 1 at negative 3 comma 5, point z sub 2 at negative 5 comma negative 2, point P at 2 comma 7, point Q at negative 2 comma negative 7, point R at negative 3 comma negative 5, point S at negative 8 comma 3 Which point represents z1 + z2? P Q R S

Answer 1

S(-8, 3)

Explanation:

In the complex plane, a complex number is represented by a point (a, b), where a is the real part and b is the imaginary part.

For example, for the complex number -3 + 5i, the real part is -3 and the imaginary part is 5i. So, we plot the ordered pair (-3, 5) to represent the complex number -3 + 5i.

To add two complex numbers, simply add their corresponding real and imaginary parts.

Given:

• z₁ = (-3, 5)
• z₂ = (-5, -2)

Therefore, the sum z₁ + z₂ is calculated as follows:

`\begin{aligned}z_1 + z_2 &= (-3 +(-5), 5+(-2))\\&=(-3-5,5-2)\\& = (-8, 3)\end{aligned}`

So, the point that represents z₁ + z₂ is:

`\Large\boxed{\boxed{S(-8, 3)}}`