Question

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

Answer 1

Answer:

None of the options are correct.

Step-by-step explanation:

Let the complex number is a + ib

Given distance from origin = 17 units

Now, by distance formula distance of a point  from the origin  =

$17 = \sqrt{(x)^{2} + (y)^{2} }$

1) Check for 2 + 15 i

here, $\sqrt{15^2 + 2^2} = \sqrt{225 + 4} = \sqrt{229}$ ≠ 17

2) Check for 17 +  i

here, $\sqrt{17^2 + 1^2} = \sqrt{289 + 1} = \sqrt{290}$≠ 17

3) Check for 20 - 3 i

here, $\sqrt{20^2 + (-3)^2} = \sqrt{400 + 9} = \sqrt{409}$≠ 17

4) Check for 4 -  i

here, $\sqrt{4^2 + (-1)^2} = \sqrt{16 + 1} = \sqrt{17}$ ≠ 17

Hence,  none of the options are correct.