simplify the following expressions involving complex numbers.
(3+2i)-(-7-i)
10 + 3i
how did you do that?
can you show me this one and explain how this time?
(3+2i)(-7-i)
or even
(3-2i)^2
you would do 3+2i=5i, then -7-i=7i then 5i+7i=12i
(3+2i)-(-7-i) =
(3+2i) + (7 + i) =
3 + 7 + 2i + i =
10 + 3i
(3+2i)*(-7-i) =
-(3+2i)*(7 + i) =
-[3*7 + 3*i + 2i*7 +2i*i] =
-[21 + 3i + 14i - 2] =
-[19 + 17i]
(3-2i)^2 =
9 - 12i - 4 =
5 - 12 i
thankyou, you are very good at math!
can you help with this one please and thankyou?
Determine the values of k if the graph of
y=2x^2-sx+3k
intersects the x-axis at 2 distinct points.
Thanks!
a x^2 + bx + c = 0 has two different roots if the discriminant D defined as:
D = b^2 - 4 a c does not equal zero.
If a, b and c are real numbers then for D > 0 there are two real roots while for D < 0 there are two complex roots.
In this problem we have to demand that D > 0 --->
D = s^2 - 24 k > 0 --->
k < s^2/24
if anyone knows the answer please help me on this one too!
To determine the values of k if the graph of y = 2x^2 - sx + 3k intersects the x-axis at two distinct points, we need to find the discriminant of the quadratic equation.
The quadratic equation can be written in the form ax^2 + bx + c = 0. In this case, a = 2, b = -s, and c = 3k.
The discriminant D is defined as D = b^2 - 4ac. If D is greater than 0, there are two real roots (two distinct points of intersection with the x-axis). If D is less than 0, there are two complex roots.
Substituting the values of a, b, and c into the discriminant formula, we get:
D = (-s)^2 - 4(2)(3k)
D = s^2 - 24k
To ensure that the graph of the quadratic equation intersects the x-axis at two distinct points, we need to have D > 0.
Therefore, we have the inequality:
s^2 - 24k > 0
To find the values of k that satisfy this inequality, we solve for k:
k < s^2 / 24
So, the values of k that make the graph of y = 2x^2 - sx + 3k intersect the x-axis at two distinct points are any values of k that are less than s^2/24.