The correct value of (3cis(pi/6))³ is 27i.
<h3>What is Complex Number?</h3>
Complex numbers are numbers that consist of two parts — a real number and an imaginary number. Complex numbers are the building blocks of more intricate math, such as algebra.
Given the complex number in polar coordinate expressed as
z = r(cos∅+isin∅)
zⁿ = {r(cos∅+isin∅)}ⁿ
According to DeMoivre’s Theorem;
zⁿ = rⁿ(cosn∅+isinn∅)
Given the complex number;
(3cis(pi/6))³
= {3(cosπ/6 + isinπ/6)}³
Using DeMoivre’s Theorem;
= 3³(cos3π/6 + isin3π/6)
= 3³(cosπ/2 + isinπ/2)
= 3³(0 + i(1))
= 27i
Thus, the correct value of (3cis(pi/6))³ is 27i.
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Answer:
A) y = 8.63 x
B) $224.38
Step-by-step explanation:
The the average monthly cost = (147.98+152.17+165.63)/3 = $155.26
So, For 18 employees the average monthly cost = $155.26
Let the equation that can be used to estimate y, the average monthly cost, in dollars, to buy lunch for x employees. ⇒ y = mx
For x = 18 , y = $155.26
So, m = y/x = $155.26/18 ≈ $8.63
∴ y = 8.63 x
To find the total cost for 26 employees.
∴ x = 26
∴ y = 8.63 * 26 = 224.38
The total cost of a monthly lunch for 26 employees = $224.38
Answer:
≈ 82 feet
Step-by-step explanation:
Since the triangle is right use Pythagoras' identity to calculate distance (d)
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.
Here the hypotenuse is the distance (d) between the 2 poles, hence
d² = 80² + 45² = 6400 + 2025 = 8425 ( take the square root of both sides )
d =
≈ 82 feet ( to the nearest foot )
Answer:
y = 3x + 1
Step-by-step explanation: