Question

Which complex number has a distance of √17 from the origin on the complex plane?
a. 2 + 15i
b. 17 + i
c. 20 - 3i
d. 4 - i

Answer 1

The distance of a complex number a+bi from the origin on the complex plane is given by the formula:
$\sqrt{a^2+b^2}$

a.
$2+15i \\ a=2 \\ b=15 \\ \Downarrow \\ d=\sqrt{2^2+15^2}=\sqrt{4+225}=\sqrt{229}$

b.
$17+i \\ a=17 \\ b=1 \\ \Downarrow \\ d=\sqrt{17^2+1^2}=\sqrt{289+1}=\sqrt{290}$

c.
$20-3i \\ a=20 \\ b=-3 \\ \Downarrow \\ d=\sqrt{20^2+(-3)^2}=\sqrt{400+9}=\sqrt{409}$

d.
$4-i \\ a=4 \\ b=-1 \\ \Downarrow \\ d=\sqrt{4^2+(-1)^2}=\sqrt{16+1}=\sqrt{17}$

The answer is D.

Answer 2

Answer:

d 4-i

Step-by-step explanation: