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
Answer:
D
Step-by-step explanation:
Whole numbers are the basic counting numbers: 
Integers are whole numbers and negative numbers: 
Rational numbers are all fractions 
where m is an integer and n is a natural number.
Irrational numbers are all real numbers that are not rational.
Number 
is irrational number (it is not counting number, so it is not whole number, not integer number), it cannot be represented as a fraction, so it is not rational number, thus this number is irrational number.
The product of integer number -2 by irrational number is irrational number 
Correct option - option D
They are all eawualateral
Answer:
B
Step-by-step explanation:
Whenever you are asked to find the number of square feet covered by something, you are finding an area. To find the area of Jason’s circle, you first need to figure out if you have been given the radius or the diameter. By definition, the diameter of a circle is the longest distance across the circle, so we know here that the diameter is 8 feet. This means that the radius is 4 feet. So...
A = π(4)2
= 16π
≈ 50.2 square feet
So, Jason’s circle will cover about 50.2 square feet of his wall (and B is the closest one to that)
6z to the 4th power - 2z to the 3rd power
