Question

Which complex number has a distance of radical 17 from the origin on the complex plane?

2+15i
17+i
20-3i
4-i

Answer 1

Answer: LAST OPTION

Explanation:

The complex numbers shown have the form:

`a+bi`

By definition, the distance can the distance of the complex number from the origin on the complex plane can be calculated with the formula shown below:

`d=√(a^2+b^2)`

Substitute values of each option. Then:

1)
`d=√(2^2+15^2)=√(229)`

2)
`d=√(17^2+1^2)=√(290)`

3)
`d=√(20^2+(-3)^2)=√(409)`

4)
`d=√(4^2+(-1)^2)=√(17)` (CORRECT OPTION)

Answer 2

The right choice is (D) 4-i

Explanation:

See the attached image