Question

Which complex number has a distance of (squareroot) of 17)) from the origin on the complex plane?

Answer 1

Answer:

$4-i$

Step-by-step explanation:

The distance of a complex number

$z=a+bi$

from the origin is given by:

$|z|=\sqrt{(a-0)^2+(b-0)^2}$

$|z|=\sqrt{a^2+b^2}$

The length of  $2+15i$ is;

$=\sqrt{2^2+15^2}$

$=\sqrt{4+225}$

$=\sqrt{229}$

The length of  $17+i$ is;

$=\sqrt{17^2+1^2}$

$=\sqrt{289+1}$

$=\sqrt{290}$

The length of  $20-3i$ is;

$=\sqrt{20^2+3^2}$

$=\sqrt{400+9}$

$=\sqrt{409}$

The length of  $4-i$ is;

$=\sqrt{4^2+1^2}$

$=\sqrt{16+1}$

$=\sqrt{17}$

The correct choice is D

Answer 2

Its "4 - i"... i just took the test