Question

which one of the points i, -2+i,and 3 is farthest from the origin

Answer 1

The farthest point from the origin among  $i, -2+i, 3$ is $3$.

Step-by-step explanation:

Given: Three points in the complex plane : $i, -2+i, 3$

To find: Farthest point from origin among these

How to find the distance of a complex number from the origin?

Let $x=a+ib$ be a complex number

The distance of  $a+ib$ from origin is given by:

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

Let us calculate the distance from the origin for each given point :

• $|i|=\sqrt{0^{2} +1^{2} }$

           $=1$

• $|-2+i|=\sqrt{(-2)^{2} +1^{2} }$

                      $= \sqrt{5}$

• $|3|=3$

Since, $1<\sqrt{5} <3$

Therefore, 3 is the farthest point from the origin.