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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The system 150x+400y=1950 and x = y+2 could be used to determine the number of small boxes and large boxes ordered where x represents the number of small boxes and y represent the number of large boxes.
Step-by-step explanation:
Given,
Number of nails in small box = 150 nails
Number of nails in large box = 400 nails
Total nails in ordered boxes = 1950 nails
Let,
x be the number of small boxes ordered.
y be the number of large boxes ordered.
According to given statement;
150x+400y=1950 Eqn 1
The contractor bought 2 more small boxes than large boxes
x = y+2 Eqn 2
The system 150x+400y=1950 and x = y+2 could be used to determine the number of small boxes and large boxes ordered where x represents the number of small boxes and y represent the number of large boxes.
Keywords: linear equation, substitution method
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Answer:
26.29 cu. in.
Step-by-step explanation:
