Answer:
4 - i is the correct option from all the others.
Step-by-step explanation:
4 - i is one of the options I choose.
First let's divide this into "a" and "b"
so, a = 4
and, b = -1
This will become : √4² + (-1)² = √16 + 1 = √17
Therefore the last option is correct from all the other.
Answer:
None of these.
Please make sure you have written the choices correctly and check the question please.
The problem and choices I see:
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
Step-by-step explanation:
A complex number, [tex]a+bi[/tex], and the point [tex]0+0i[/tex] has distance:
[tex]\sqrt{(a-0)^2+(b-0)^2}[/tex] by distance formula.
Simplifying this gives us:
[tex]\sqrt{a^2+b^2}[/tex]
So we are looking for [tex]a \text{ and } b[/tex] in your choices so that [tex]\sqrt{a^2+b^2}=17[/tex].
Let's begin.
Choice 1: [tex]2+15i[/tex]
[tex]a=2[/tex]
[tex]b=15[/tex]
So [tex]\sqrt{2^2+15^2}=\sqrt{4+225}=\sqrt{229}\approx 15.1327[/tex].
So choice A is out if I interpreted it correctly.
Choice 2:[tex]17+i[/tex]
[tex]a=17[/tex]
[tex]b=1[/tex]
So [tex]\sqrt{17^2+1^2}=\sqrt{289+1}=\sqrt{290}\approx 17.0294[/tex].
So choice B is out.
Choice 3: [tex]20-3i[/tex]
[tex]a=20[/tex]
[tex]b=-3[/tex]
So [tex]\sqrt{20^2+(-3)^2}=\sqrt{400+9}=\sqrt{409}\approx 20.2237[/tex]
So choice C is out.
Choice 4: [tex]4-i[/tex]
[tex]a=4[/tex]
[tex]b=-1[/tex]
So [tex]\sqrt{4^2+(-1)^2}=\sqrt{16+1}=\sqrt{17}\approx 4.1231[/tex]
So choice D is out.
So it would be none of these have a distance of 17 from the origin.
