ANSWER
x = ±1 and y = -4.
Either x = +1 or x = -1 will work
EXPLANATION
If -3 + ix²y and x² + y + 4i are complex conjugates, then one of them can be written in the form a + bi and the other in the form a - bi. In other words, between conjugates, the imaginary parts are same in absolute value but different in sign (b and -b). The real parts are the same
For -3 + ix²y
⇒ real part: -3
⇒ imaginary part: x²y
For x² + y + 4i
⇒ real part: x² + y (since x, y are real numbers)
⇒ imaginary part: 4
Therefore, for the two expressions to be conjugates, we must satisfy the two conditions.
Condition 1: Imaginary parts are same in absolute value but different in sign. We can set the imaginary part of -3 + ix²y to be the negative imaginary part of x² + y + 4i so that the
x²y = -4 ... (I)
Condition 2: Real parts are the same
x² + y = -3 ... (II)
We have a system of equations since both conditions must be satisfied
x²y = -4 ... (I)
x² + y = -3 ... (II)
We can rearrange equation (II) so that we have
y = -3 - x² ... (II)
Substituting into equation (I)
x²y = -4 ... (I)
x²(-3 - x²) = -4
-3x² - x⁴ = -4
x⁴ + 3x² - 4 = 0
(x² + 4)(x² - 1) = 0
(x² + 4)(x-1)(x+1) = 0
Therefore, x = ±1.
Leave alone (x² + 4) as it gives no real solutions.
Solve for y:
y = -3 - x² ... (II)
y = -3 - (±1)²
y = -3 - 1
y = -4
So x = ±1 and y = -4. We can confirm this results in conjugates by substituting into the expressions:
-3 + ix²y
= -3 + i(±1)²(-4)
= -3 - 4i
x² + y + 4i
= (±1)² - 4 + 4i
= 1 - 4 + 4i
= -3 + 4i
They result in conjugates
0.50 24 times is the answer just multiply them
Answer:
109410480 dates.
Step-by-step explanation:
We can find 555*888*222 different dates = 109410480 dates.
This is because we can find the total number of combinations between the different choices by multiplying the numbers of each different factor.
Hope this helped!
Mean=10.4 since you add all the numbers which gives you 94 and divide by how many they are and that is 9
median=13 (middle number)
mode=14 constant seen number
range= 11 because 15 minus 4 is 11 (difference between your lowest and highest value
a line plot is another word for dot plot so just use 1 -20 and arrange the number
hope this helps
So first, find the area of the square. 12x12= 144inches^2
Then find the area of the circle. To do this we use pi x r^2. The radius of the circle is 6 inches. Pi x 6^2 = 113.04inches^2.
144 - 113.04 = 30.6, so your answer is 30.6 inches^2
The circles circumference is worked out by using pi x d. The diameter is 12 inches, so 3.14x12 = 37.68 inches.
The squares perimeter is 12 x 4 = 48 inches.
If you round up the circumference of the circle to the nearest integer, you get 38 inches. The ratio would therefore be, 38:48, which can be rounded down to 19:24 :)
