Okay so i am having some trouble with a few problems.
What is the radius of the circle whose equation is x^2 + y^2 +18x + 12y + 36=0
1)9
2)3*radical 17
3)81
4)153
Next Problem:
What is the magnitude of the vector resulting from graphing the complex number 3-4i?
1) -5
2) radical -5
3) radical 5
4) 5
Please help even if you can only answer 1 of them, i would greatly appreciate it!
What is the radius of the circle whose equation is x^2 + y^2 +18x + 12y + 36=0
1)9
2)3*radical 17
3)81
4)153
Next Problem:
What is the magnitude of the vector resulting from graphing the complex number 3-4i?
1) -5
2) radical -5
3) radical 5
4) 5
Please help even if you can only answer 1 of them, i would greatly appreciate it!
-
The standard form of the equation of a circle is:
(x - h)^2 + (y - k)^2 = r^2
where r is the radius and (h, k) is the center.
To solve this problem, you have to complete the square on the x and y terms. I won't go through the process, but the end result is:
x^2 + y^2 + 18x + 12y + 36 = 0
⇔ (x + 9)^2 + (y + 6)^2 = 81
Leaving you with a radius of r = √81 = 9.
For the second one, are you knowledgeable about vectors, in general? The graph of a complex number is just a vector with the real part as the horizontal component and the imaginary part as the vertical component. In other words,
3 - 4i = <3, -4>
The magnitude is then just the distance from (0, 0) to (3, -4). If you know your Pythagorean triples, then you should recognize the magnitude as 5. If not, applying the Pythagorean theorem (aka distance formula):
|3 - 4i|
= √(3^2 + 4^2)
= √25
= 5
Since magnitude is distance, we don't use negative numbers, so -5 would be an unacceptable answer.
(x - h)^2 + (y - k)^2 = r^2
where r is the radius and (h, k) is the center.
To solve this problem, you have to complete the square on the x and y terms. I won't go through the process, but the end result is:
x^2 + y^2 + 18x + 12y + 36 = 0
⇔ (x + 9)^2 + (y + 6)^2 = 81
Leaving you with a radius of r = √81 = 9.
For the second one, are you knowledgeable about vectors, in general? The graph of a complex number is just a vector with the real part as the horizontal component and the imaginary part as the vertical component. In other words,
3 - 4i = <3, -4>
The magnitude is then just the distance from (0, 0) to (3, -4). If you know your Pythagorean triples, then you should recognize the magnitude as 5. If not, applying the Pythagorean theorem (aka distance formula):
|3 - 4i|
= √(3^2 + 4^2)
= √25
= 5
Since magnitude is distance, we don't use negative numbers, so -5 would be an unacceptable answer.