Question

Which complex number is a distance of sqrt17 from the origin on the complex plane?

A. 2 + 15i
B. 17 + i
C. 20 - 3i
D. 4 - i

Answer 1

Let z=x+iy be a complex number. The distance from this complex number to the origin is

`√((x-0)^2+(y-0)^2)=√(x^2+y^2).`

Consider all options:

A. z=2+15i, then
`√(2^2+15^2)=√(229).`

B. z=17+i, then
`√(17^2+1^2)=√(290).`

C. z=20-3i, then
`√(20^2+(-3)^2)=√(409).`

D. z=4-i, then
`√(4^2+(-1)^2)=√(17).`

Answer: correct choice is D.