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

Well, we don't know what quadrant it's in, so we don't know
which part is the real one and which part is the imaginary one,
and we also don't know the signs of the real or imaginary parts.

Now that I think about it, we don't even know the angle. 
The point in the complex plane can be any point on the circle
that's centered at the origin and has a radius of 17. 

So I can give you the complex number like this:

It can be ANY complex number       A + iB
as long as 'A' and 'B' meet these
requirements:

-- 'A' and 'B' can both be positive or negative

--  A² + B²  =  17.

There are an infinite number of possibilities.
A few of them are ...

-1 + 4i
-1 - 4i
1 + 4i
1 - 4i
-4 + i
-4 - i
4 + i
4 - i

√6 + i√11 = 17

etc.

None liner bro because