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 sums range from 2 to 12 of which 6 are even out of 11 possible sums.
There are 4 multiples of 3, two of which are odd.
So the number of even sums is 6 and there are 2 unique or odd multiples of 3.
So there are a total 6+2=8 outcomes we want out of 36 possible outcomes.
The probability is then 8/36 or 2/9
12/5 is the answer!
Hope I helped!
Ps: symbolab.com is a great calculator to help solve those type of problems :-)
Answer:
Step by step explanation:
Answer: Width of canvas = 9 inches
Area left for painting after painting the border = 70 square inches.
Explanation :
Since we have given that
Area of painting = 108 square inches
Length of canvas = 12 inches
As we know that
So, breadth of canvas = 9 inches .
Now, Chloe paints a 1 inch wide blue border on the canvas.
Hence, remaining area = 70 square inches .
