Answer: A, B, C, and E
Step-by-step explanation:
If both sides are real numbers, then the product will be a real number.
If in at least one of the sides we have a complex number, then the product will be real if:
The other number is zero.
The other number is the conjugate of the first.
This is when:
Suppose we have a number:
z = a + b*i
The conjugate will be:
w = a - b*i
And the product between them is:
(a + b*i)*(a - b*i) = a^2 + a*b*i - a*b*i + b^2 = a^2 + b^2
Then the options that will have a real answer are:
A. (4+5i)(4-5i) = 4^2 + 5^2 = 16 + 25 = 41
B. (4 + 91)*(41 - 9) = 3040
C. (3 + 2*i)*(3 -2*i) = 3^2 + 2^2 = 9 + 4 = 13
E. (312 + 7i)*(312 - 7i) = 312^2 + 7^2 = 97,393
Answer:
-3
Step-by-step explanation:
Answer:
Area of polygon = 18
Step-by-step explanation:
the given points are :
Point A (2.5)
Point B (8,5)
Point C (8,9)
Point D (5,7)
Point E (2,9)
Firstly , create the array
A 2 5
B 8 5
C 8 9
D 5 7
E 2 9
A 2 5
Now,
Multiply the x coordinates of each vertex by the y coordinate of the next vertex . and then add the result.
⇒ 10 + 72 + 56 + 45 + 10 = 193 .......(1)
Now,
Multiply the y coordinate of each vertex by the x coordinate of next vertex. then add the result
⇒ 40 + 40 + 45 + 14 + 18 = 157 ........(2)
Now, Subtract equation (2) from equation (1), we get
193 - 157 = 36
Now, Divide by 2 to get the area of polygon
∴ we get
Area of polygon = 18
Answer:
Pretty sure its (D). Yes, half of the residuals are positive and half are negative.
Yes, I am verifying my own answers for people who don't like to be trolled.
A is wrong, I put it in wrong the first time. D also makes sense now that I look at it more. I got an 88%
ED2021
