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

A complex number requires a real number and an imaginary number

Ex: 3 + 4i

The distance from the origin of a complex number uses the Pythagorean Theorem: a^2 + b^2 = c^2

With this example (3 + 4i) a = 3, b = 4, and c = distance from origin

(3) ^2 + (4) ^2 = c^2

But in this problem, we have c, but not a or b

a^2 + b^2 = (sqrt (17)) ^2

sqrt (17) ^2 = 17

a^2 + b^2 = 17

Start trying integers for a starting at 1

a = 1: (1) ^2 + b^2 = 17 1 + b^2 = 17 b^2 = 16 b = 4

a = 1, b = 4 works in this case, so a possible answer is

1 + 4i