Which complex number is farthest from the origin in the complex plane? A −5+i B −2+4i C 3 + 3i D 4 + 3i

Option A: −5+i

Step-by-step explanation:

In the complex plane, the real part of the number is expressed in the horizontal axis, and the imaginary part is expressed in the vertical axis. So, to find the distance of a point to the origin, we just need to apply the distance formula with the second point being (0,0):

A. −5+i

real part: -5

imaginary part: 1

distance to origin: D = sqrt((-5)^2 + 1^2) = 5.099

B. −2+4i

real part: -2

imaginary part: 4

distance to origin: D = sqrt((-2)^2 + 4^2) = 4.4721

C. 3 + 3i

real part: 3

imaginary part: 3

distance to origin: D = sqrt(3^2 + 3^2) = 4.2426

D. 4 + 3i

real part: 4

imaginary part: 3

distance to origin: D = sqrt(4^2 + 3^2) = 5

So the farthest point from the origin is point A: −5+i

domain is all the x values included in the

0 ≤ x ≤ 2

range is all the y values of the graph

-2 ≤ y ≤ 2

***keep in mind that there are different ways to show domain and range

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figure c

step-by-step explanation:

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