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
Monday
Tuesday
Wednesday
Thursday
Blink
Monday
That’s so true XD
Based on the fact that Sienna has read 60 pages, we can infer that Micha has read 375 pages of the book.
Sienna has read 40% of what Rhys has read and that corresponds to 60 pages. The number of pages read by Rhys is therefore:
<em>= Number of pages / Percentage read </em>
= 60 / 40%
= 150 pages
The 150 pages read by Rhys is 40% of what Micah has read. Micah has therefore read:
= 150 / 40%
= 375 pages
In conclusion, Micah has read 375 pages.
<em>Find out more at brainly.com/question/2807698.</em>
Answer:
The correct answer is last option 78.5%
Step-by-step explanation:
Points to remember
Area of circle = πr²
Where r is the radius of circle
Area of square = a²
Where 'a' is the side length of square
<u>To find the area of circle</u>
Here r = 10 cinches
Area = πr²
= 3.14 * 10²
= 3.14 * 100 = 314
<u>To find the area of square</u>
Here a = 20 inches
Area = a²
= 20²
= 400
<u>To find the probability percentage</u>
Probability = area of circle/Area of square
= (314/400)*100
78.5 %
Answer:
11
Step-by-step explanation:
