Question

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

Answer 1

Answer:

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