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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7 0

2 years ago

Luke's water bottle holds 2,150 milliliters. He drinks 3.5 bottles of water each day. How many milliliters of water does he drin

sashaice [31]

Answer:

7525 milliliters

Step-by-step explanation:

because if you multiply 2150 by 3.5 you will get that number

4 0

2 years ago

X2 - 2x + 1 = 0? Please answer fast I need it now

JulsSmile [24]

Answer:

Step-by-step explanation:

x2 - x2 = 0

+1 = 1

3 0

3 years ago

Please help please these are short answers

atroni [7]

Answer: The answers are given below.

Step-by-step explanation: The calculations are as follows:

(19) Weight of the puppy last week is

$W_\ell=2\dfrac{1}{2}~\textup{lb},$

and weight of the puppy this week is

$W_p=7\dfrac{1}{4}=\dfrac{29}{4}~\textup{lb}.$

Therefore, the weight gained by the puppy is given by

$W_g=W_p-W_\ell=\dfrac{29}{4}-\dfrac{5}{2}=\dfrac{29-10}{4}=\dfrac{19}{4}=4\dfrac{3}{4}~\textup{lb}.$

(20) Time taken in Route 1 = 1 hour 30 minutes.

Time taken in Route 2 = 1 hour 45 minutes.

Time taken in Route 3 = 1 hour 35 minutes.

Time taken in Route 4 = 1 hour 25 minutes.

Since we want to spent the least amount of time on the bus, so we will be taking route 4.

(21) Time taken by Nazia to complete her language arts homework is

$H_\ell=\dfrac{4}{9}~\textup{hr},$

and the time taken by Nazia to complete her Mathematics homework is

$H_m=\dfrac{2}{9}~\textup{hr}.$

Therefore, Nazia takes more time to complete Language Arts homework, by

$H=H_\ell-H_m=\dfrac{4}{9}-\dfrac{2}{9}=\dfrac{2}{9}~\textup{hr}.$

(22) Quantity of Aluminium collected by Maya is

$A_m=\dfrac{4}{20}=0.2~\textup{lb},$

and the quantity of Aluminium collected by her friend Abigail is

$A_a=\dfrac{7}{8}=0.87~\textup{lb}.$

Therefore,

(a) Abigail collected more aluminium

and

(b) Total Aluminium collected by both the girls is

$T=A_m+A_a=\dfrac{4}{20}+\dfrac{7}{8}=\dfrac{8+35}{40}=\dfrac{43}{40}~\textup{lb}.$

(23) Quantity of snow fall last Wednesday is

$S_w=3\dfrac{1}{4}=3.25~\textup{in.},$

and quantity of snowfall on sunday is

$S_s=3\dfrac{4}{5}=3.8~\textup{in.}.$

Therefore, quantity of snowfall was more on Sunday by

$S=S_s-S_w=3\dfrac{4}{5}-3\dfrac{1}{4}=\dfrac{19}{5}-\dfrac{13}{4}=\dfrac{76-65}{20}=\dfrac{11}{20}~\textup{in.}.$

Thus, all the questions are answered.

3 0

3 years ago