Which statement describes the geometric construction of the product zw on the complex plane?
No statements are given...
At the very least, we can compute the product zw by multiplying the moduli and adding the arguments. That is, if
z = 8 (cos(π/3) + i sin(π/3))
w = 3 (cos(π/6) + i sin(π/6))
then their product is
zw = 8•3 (cos(π/3 + π/6) + i sin(π/3 + π/6))
zw = 24 (cos(π/2) + i sin(π/2))
zw = 24i
The product of complex numbers z and w results in a point that is situated along the positive y-axis in the complex plane, being 24 units away from the origin.
In complex numbers, the geometric meaning of a product of two numbers, here zw, corresponds to the multiplication of the moduli and the addition of the arguments of the two numbers.
Here, z = 8(cos (pi/3) + i sin (pi/3)) and w = 3(cos(pi/6) + i sin (pi/6)), so the modulus of zw is 3*8 = 24.
The argument is the sum of the arguments (pi/3 + pi/6) which is pi/2. Hence, the product can be rewritten as zw = 24(cos(pi/2) + i sin(pi/2)). This geometric construction will situate the point along the positive y-axis in the complex plane, with a distance of 24 units from the origin.
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Answer: y = 2
Step-by-step explanation:
First, we combine like terms.
7y-4y = 6
Since the terms are already combined, we can solve this equation.
First, we do 7y-4y.
7y-4y = 6
3y = 6
Now, we solve for y.
3y = 6
y = 6/3
y = 2
To solve the equation 7y - 4y = 6 for y, we first simplify the left side to get 3y = 6. Then we divide both sides by 3 to get y = 2.
The given problem is a simple algebraic equation which we need to solve for y. The equation given is 7y - 4y = 6.
First, we simplify the left side of the equation by subtracting the coefficients of y: 7y - 4y equals 3y. So our equation is now 3y = 6.
To get y by itself on the left side of the equation, we need to divide both sides of the equation by 3. This gives us: y = 6/3 .
Therefore, the value of y that satisfies the equation is y = 2.
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Answer:
Volume = 680 ft³
Step-by-step explanation:
Given
Floor Area = 85 ft²
Height = 8 ft
Required
Volume of the Kitchen
To solve this, it'll be assumed that Tony's kitchen has a regular shape.
Having said that, the volume of Tony's kitchen is calculated as thus.
Volume = Floor Area * Height.
Substitute the values of floor area and height
Volume = 85ft² * 8ft
Volume = 680 ft³
Hence, the volume of Tony's kitchen is 680ft³