Question

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

2 + 15i
17 + i
20 – 3i
4 – i

Answer 1

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

Answer 2

`4-i`

Explanation:

The distance of a complex number

`z=a+bi`

from the origin is given by:

`|z|=√((a-0)^2+(b-0)^2)`

`|z|=√(a^2+b^2)`

The length of
`2+15i` is;

`=√(2^2+15^2)`

`=√(4+225)`

`=√(229)`

The length of
`17+i` is;

`=√(17^2+1^2)`

`=√(289+1)`

`=√(290)`

The length of
`20-3i` is;

`=√(20^2+3^2)`

`=√(400+9)`

`=√(409)`

The length of
`4-i` is;

`=√(4^2+1^2)`

`=√(16+1)`

`=√(17)`

The correct choice is D