An equation of the form z= a+ib, where a and b are real numbers, is defined to be a complex number. The real part is denoted by Re z = a and the imaginary part is denoted by Im z = ib.
Now, According to the question:
Let's know:
What are Complex Numbers?
A complex number is the sum of a real number and an imaginary number. A complex number is of the form a + ib and is usually represented by z. Here both a and b are real numbers. The value 'a' is called the real part which is denoted by Re(z), and 'b' is called the imaginary part Im(z). Also, ib is called an imaginary number.
Representation of the Complex Numbers:
z = a + ib
'a' represent the Real part
'ib' represent imaginary number and imaginary part.
Some of the examples of complex numbers are :
2 + 3i , -3 - 4i , 1/2 + 1/3i etc.
Power of i
The alphabet i is referred to as the iota and is helpful to represent the imaginary part of the complex number. Further the iota(i) is very helpful to find the square root of negative numbers. We have the value of [tex]i^2[/tex] = -1, and this is used to find the value of √-4 = √[tex]i^2[/tex]4 = ±2i The value of [tex]i^2[/tex] = -1 is the fundamental aspect of a complex number. Let us try and understand more about the increasing powers of i.
i = √-1[tex]i^2[/tex] = -1[tex]i^3[/tex] = i.[tex]i^2[/tex] = i(-1) = -i[tex]i^4[/tex] = [tex](i^2)^2[/tex] = [tex](-1)^2[/tex] = 1[tex]i^4^n[/tex] = 1[tex]i^4^n^+^1[/tex] = i[tex]i^4^n^+^2[/tex] = -1[tex]i^4^n^+^3[/tex] = -iLearn more about Complex numbers at:
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Alex and Dave sell donuts. Alex earns $11 more than Dave. Let x represent the number of donuts Dave sells. Let y represent the total amount of donuts Alex sells. Which equation shows this relationship
Answer:
y = x + 11
Step-by-step explanation:
x = Number of donuts Dave sells
y = Total amount of donuts Alex sells
Amount earned by Alex = $11 more than Dave's earning
This means y is greater than x by $11
Total amount of donuts Alex sells = Number of donuts Dave sells + $11
y = x + 11
Noah spent $66 for 20 gallons of gasoline. Lydia spent $81.25 for 25 gallons of gasoline. How much did each person spend for 1 gallon of gasoline?
Answer:
Noah spent $3.3 for 1 gallon of gasoline.
Lydia spent $3.25 for 1 gallon of gasoline.
Step-by-step explanation:
To find how much each person spent for 1 gallon of gasoline, we divide the amount spent by the number of gallons.
Noah spent $66 for 20 gallons of gasoline.
Amount spent $66, 20 gallons. So
66/20 = $3.3
Noah spent $3.3 for 1 gallon of gasoline.
Lydia spent $81.25 for 25 gallons of gasoline.
Amount spent $81.25, 25 gallons. So
81.25/25 = $3.25
Lydia spent $3.25 for 1 gallon of gasoline.
There are 150 politicians at a meeting.
They each shake hands with everyone
else. How many handshakes were there?
PLEASE HELP ASAP
Answer:
11175Step-by-step explanation:
Person 1 will shake hands with 149 othersPerson 2 ... 148 (excluding the first person)Person 2 ... 147 (excluding the first two persons)...Person 149 ... 1 (with person 150)Person 150 ... none (already had 149 handshakes)Total handshakes:
1 + 2 + ... 149 = 149(1 + 149)/2 = 111753 Yolanda asks a random sample of 50 students at her school what they do after
school. Of the 50 students, 30 say they play a sport. Based on the sample, about
what percent of students at Yolanda's school play a sport after school?
A 15%
B 30%
C 50%
D 60%
I WILL GIVE BRAINLIEST AND SEND 50 POINTS IF GOOD no copying from internet
What do you know about the angles of a right triangle?
A all angles might be right angles.
B only one angle is a right angle and the other two are acute
C one or more angles must be right angles
D only one angle is a right angle and the other two are obtuse
Answer:
B
Step-by-step explanation:
Answer:
B only one angle is a right angle and the other two are acute
Step-by-step explanation:
its clear from looking at an angle lol
Create and solve a 2 step equation with addition and division.
PLEASE HELP THIS IS DUE TODAY!!! .-.
Answer:
(2+4)÷12
Step-by-step explanation:
jxkgxljcluckyxlhlusgibibsi do u need an explanation but here
Please help me out 5 points the first person
Answer:
(6,5) is an ordered pair to this question.
[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]
1st we have to go right to the origin 6
x=6then up to 5
y=5According to the question,
coordinate
=(x,y)=(6,5)insaley easy 4th grade homework math question i will mark brainliest
Answer:
first answer 20
Second answer 1/2
For the last on I think it’s 1/4
Step-by-step explanation:
Lol Sorry if I’m wrong
Answer:
1. 5 1/4 or 5.25 or 21/4
2. 1/2
3. Im not sure but i think it's 1 1/2 becouse 1 1/2 divided by 2 = 3/4 or 0.75
Step-by-step explanation:
what is the domain of f?
HELP PLEASE
Answer:
-7 to 7
Step-by-step explanation:
it is the range of the x values
How do I show my work for this and get the answer? Thanksss
Answer:
the answer for this problem is 135
Help me please! I need this done quick!
Answer:
1. 15
2. 26
3. [tex]\sqrt{58[/tex]
4. 8
5. 6[tex]\sqrt{15[/tex]
6. [tex]\sqrt{2[/tex]
7. [tex]\sqrt{377[/tex]
8. 18
9. x = [tex]\sqrt{106[/tex]
y = [tex]\sqrt{34[/tex]
Step-by-step explanation:
IM TIRED DO I HAVE TO EXPLAIN?
I need help pls:(((((((((((((((((
Answer:
108
Step-by-step explanation:
We first must find the total per year of every family.
Remember... there are 12 months in a year
Wilson: 18 × 12 = 216
Kumar: 16 × 12 = 192
Lopez: 27 × 12 = 324
Anders: 14 × 12 = 168
Johnson: 15 × 12 = 180
The Lopez family borrows the most. (324 books)
The Wilson family borrows the second most. (216 books)
324 - 216 = 108
Solve for x. You must show all of your work to receive credit.
V
5x + 17
23x - 5
W
37x + 5
A cable 13 meters long runs from the top of a utility pole to a point on the ground 5 meters from the base of the pole. How tall is the utility pole?
Answer:
height of the utility pole = 12 meters
Step-by-step explanation:
It is simple application of Pythagoras theorem.
In the given case, Length of cable (Hypotenuse) H = 13 meters, distance between base of pole to the point on the ground(Base) B = 5 meters and height of pole ( Perpendicular) P form a right angle triangle.
The applying Pythagoras theorem.
H^2 = P^2 +B^2
⇒ P^2 = H^2-B^2 = 13^2-5^2 = 144
⇒ P = 12 meters
hence, height of the utility pole = 12 meters
Probability of rolling a factor of 4 on the first die
Answer:
should be like 1 out of 6 chances
Step-by-step explanation:
which is proportion can be used to be determine to length of bc
Answer:
4/5=bc/8
Step-by-step explanation:
can someone help me this is a life or death question
Answer:
3 is vertical angles
1 is same side interior
2 is corresponding angles
4 is straight angles
Step-by-step explanation:
Please hurry it’s 50 seconds left
Answer:
[tex]50^{o}[/tex]
Step-by-step explanation:
Answer:
50
Step-by-step explanation:
Add 40 degrees to the 90 degrees and that will become 130 and all triangles add up to 180 so subtract 130 from 180 and you'll be left with 50
Reggie cuts 2 feet from a 9-foot length of rope. Then he cuts 14 inches from the rope. How many inches of rope are left?
Answer:
He is left with 5 feet and 10 inches.
The wood family consumes 20 bags of milk in 4 weeks.How much milk will the family require for 8 weeks?
Answer:
4
Step-by-step explanation:
If 20 jugs is in 4 weeks, and 8 weeks is 2 times as much as 4. So you would multiply 20x2 because 8 weeks is 2 times as much as 4
Find x. Please help with this problem!!!!!
in one town there are 240 boys and 260 girls who play sports of these 1/5 plays soccer. how many kids play soccer in all Hi there
Answer:
100 kids.
Step-by-step explanation:
First you add 240+260=500
Then you take 1/5 of 500 which is 100.
Hope this helps!
What is 127% of 40????
Answer:
50.8
Step-by-step explanation:
L Practice & Problem Solving
QU
11.6.PS-15
You want to wrap a gift shaped like the regular triangular prism shown. How many
square inches of wrapping paper do you need to completely cover the prism?
Answer:
xjxjxjzjzjxxjxjxjxjx
A health club charges a $75 membership fee. Weasley has $300 to spend on a health club membership. Write an inequality to model the number of months that Weasley can afford to be a member of the health club. What is the maximum number of months that he can use the health club?
Answer:
4 months
Step-by-step explanation:
we take $300 ÷$75 which is per month
then we get 4 , which is our months
The graph of y = Ab^x, where A and b are
constants, passes through (2, 2) and
(5, 16). Find the value of A and of b.
Answer:
A = 1/2, b = 2
Step-by-step explanation:
Inputting (x, y) into y = Ab^x we know that
point (2, 2):
2 = Ab^2
point (5, 16):
16 = Ab^5
So:
16/2 = Ab^5 / Ab^2
8 = b^3
b = 2
Now inputting point (2, 2) with b = 2
2 = A*2^2
2 = 4A
A = 1/2
A cone has a volume of 18 in3. Select all of the possible dimensions for the cone.
Diameter 1 in., height 18 in.
Diameter 6 in., height 6 in.
Diameter 3 in., height 6 in.
Diameter 6 in., height 3 in.
Diameter 3 in., height 24 in.
Answer: with these values I don't find any of cones
Step-by-step explanation: volume is 1/3 x pi x r^2 x h
And radius r = diameter/2. Is you round pi/3 =1 it's easier.
Possible measures: d=2 and h=18
D= 4 and h= 4.5 or d= 6 and h=2
Hollis put a layer of boxes in the bottom of a container. Each box has a volume of 1 cubic foot. The base layer of boxes in the container in shown. Hollis will need 8 of these layers to completely fill the container. What is the volume of the container in cubic feet?
Answer:
288 ft³
Step-by-step explanation:
Given that
The volume of each box is 1 cubic foot
And, Hollies required 8 of these layers
Now based on the above information
We assume that the dimension of the base layer is 6 by 6
So, the volume of the container is
= Length × Width × Height
where,
Length = 6 ft
Width = 6 ft
And, Height = 8 ft
So,
= 6 ft × 6 ft × 8 ft
= 288 ft³
Someone please help me I’ll give out brainliest please dont answer if you don’t know
Answer:
x = 2
Step-by-step explanation:
Hope this helps you!
Have a nice day <3
Answer:
Step-by-step explanation:
4x+6+3=17
Add the numbers :6+3=9
4x+9=17
Subtract 9 from both sides
4x+9-9=17-9
Simplify;
4x=8
Divide both sides by 4
4x/4=8/4
Simplify
x=2
Answered by NONE other than the ONE & ONLY #QUEEN herself aka #$$$DRIPPQUEENMO!!!
HOPE THIS HELPED!!!
An electrical engineer has an annual income of $143,482 and will pay a 6% income tax rate. What is the amount of income tax in dollars and cents that the engineer will have to pay?
Answer:
$8608.92
Step-by-step explanation:
Given data
Annual income= $143,482
Rate= 6%
We want to find 6% of $143,482
=6/100*143482
=0.06*143482
=$8608.92
Hence the income tax is
$8608.92