Question

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

Answer 1

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

$\sqrt{(x-0)^2+(y-0)^2}=\sqrt{x^2+y^2}.$

Consider all options:

A. z=2+15i, then $\sqrt{2^2+15^2}=\sqrt{229}.$

B. z=17+i, then $\sqrt{17^2+1^2}=\sqrt{290}.$

C. z=20-3i, then $\sqrt{20^2+(-3)^2}=\sqrt{409}.$

D. z=4-i, then $\sqrt{4^2+(-1)^2}=\sqrt{17}.$

Answer: correct choice is D.