Answer:
[tex]4-i[/tex]
Step-by-step explanation:
The distance of a complex number
[tex]z=a+bi[/tex]
from the origin is given by:
[tex]|z|=\sqrt{(a-0)^2+(b-0)^2}[/tex]
[tex]|z|=\sqrt{a^2+b^2}[/tex]
The length of [tex]2+15i[/tex] is;
[tex]=\sqrt{2^2+15^2}[/tex]
[tex]=\sqrt{4+225}[/tex]
[tex]=\sqrt{229}[/tex]
The length of [tex]17+i[/tex] is;
[tex]=\sqrt{17^2+1^2}[/tex]
[tex]=\sqrt{289+1}[/tex]
[tex]=\sqrt{290}[/tex]
The length of [tex]20-3i[/tex] is;
[tex]=\sqrt{20^2+3^2}[/tex]
[tex]=\sqrt{400+9}[/tex]
[tex]=\sqrt{409}[/tex]
The length of [tex]4-i[/tex] is;
[tex]=\sqrt{4^2+1^2}[/tex]
[tex]=\sqrt{16+1}[/tex]
[tex]=\sqrt{17}[/tex]
The correct choice is D
