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forsale [732]
3 years ago
8

Write answer using only positive exponents

Mathematics
1 answer:
artcher [175]3 years ago
3 0
I hope this helps you




-2^-7.w^-7



-128.1/w^7
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Find the real numbers x and y if -3+ix^2y and x^2+y+4i are conjugate of each other. Pls solve with the steps
Firdavs [7]
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
4 0
3 years ago
Read 2 more answers
Q = 15<br> a = 16<br> What would you do with q and a to get 240?
ch4aika [34]

You multiply Q and a to get 240, because 15 x 16 = 240.

6 0
3 years ago
400 reduced by 3 times my age is 163
Blababa [14]
400 - 3x = 163

Add 3x to both sides.

400 = 163 + 3x

Subtract 163 to both sides.

237 = 3x

237/3 = 79
5 0
3 years ago
The equation for the circle is (x-2)^2 + (y-1)^2 = 4<br><br> True<br> or<br> False???
jasenka [17]
True because the center is (2,1) and radius is 2
8 0
2 years ago
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What is the perimeter of a square which has the same area as a circle with circumference of 4π?
Contact [7]
The circumference of a circle is given by: 2πr, where r is the radius of the circle. Equating 4π, we have 2πr = 4π so the radius of the circle is: r = 4/2 = 2. Then, the area of the circle is given by πr ^ 2 = π * (2 ^ 2) = 4π.Since the square and the circle have the same area, then: Let L be the side of the square, we have:  L ^ 2 = 4π, clearing L = 2 * (π ^ (1/2))The perimeter of a square is the sum of its sides:  P = L + L + L + L = 2 * (π ^ (1/2)) + 2 * (π ^ (1/2)) + 2 * (π ^ (1/2)) + 2 * (π) ^ (1/2))  P = 8 * (π ^ (1/2))
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