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:
Commutative property of multiplication.
Step-by-step explanation:
This property says that changing the order of factors doesn't change the product.
Here 5×3 will be 15..... If we interchange the places of 3 & 5 , still then the product will remain same i.e. 3×5 = 15
Answer:
5,3
Step-by-step explanation:
Simplify both sides of the equation
Isolate the variable
They have the same value even though their numerator and denominator are different. For example, 8/16 and 1/2 are equivalent fractions which both represent 0.5.
Answer:
Step-by-step explanation:
Mr. Rives' rotating sprinkler waters his lawn up to a radius of 7 feet. The formula for determining the area of a circle is expressed as
Area = πr²
Where
π is a constant whose value is 3.14.
r represents the radius if the circle.
The area covered by one of Mr. Rives' rotating sprinkler would be
3.14 × 7² = 3.14 × 49 = 153.86ft²
Therefore, the maximum area of lawn that two sprinklers can cover would be
153.86 × 2 = 307.72 ft²
