Answer:
4 -i
Step-by-step explanation:
For your condition to be met, neither the real part nor the imaginary part can exceed √17 in magnitude. That excludes the first three answer choices.
The magnitude of 4-i is ...
√(4^2 +(-1)^2) = √17.
Answer:
Step-by-step explanation:
First, we need to know that a complex number, which has a real part and an imaginary part, it's like a vector, where the horizontal coordinate is the real part, and the vertical coordinate is the imaginary part.
So, to find the distances we applied the conventional definition:
[tex]d=\sqrt{r^{2}+i^{2} }[/tex]
Where [tex]r[/tex] refers to the real part and [tex]i[/tex] refers to the imaginary part.
So, we test each answer and see which one gives us the root of 17.
[tex]d=\sqrt{2^{2}+15^{2} }=\sqrt{4+225}=\sqrt{229}[/tex]
[tex]d=\sqrt{17^{2}+1^{2} }=\sqrt{290}[/tex]
[tex]d=\sqrt{20^{2}+(-3)^{2} }=\sqrt{409}[/tex]
[tex]d=\sqrt{4^{2}+(-1)^{2} }=\sqrt{17}[/tex]
Therefore, the right answer is the last one, because the distance is the squared root of 17.
