Step-by-step explanation:
(a + bi)^2 = (a + b)(a − b) + 2abi
= a² + (bi)² + 2 * a * bi
= a² + b²i² + 2abi
= as i² = -1
= a² - b² + 2abi
= (a + b) (a - b) + 2abi
The equation ( a + bi )² is simplified as A = ( a + b ) ( a - b ) + 2abi
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
A = ( a + bi )² be equation (1)
On simplifying the equation , we get
A = ( a )² + ( ib )² + 2iab
Now , the value of i² = -1
A = a² + i²b² + 2iab
Substituting the value of i in the equation , we get
A = a² - b² + 2iab
Now , the value of ( a² - b² ) = ( a + b ) ( a - b )
Substituting the values in the equation , we get
A = ( a + b ) ( a - b ) + 2iab
Therefore , the value of A is ( a + b ) ( a - b ) + 2iab
Hence , the equation is ( a + b ) ( a - b ) + 2abi
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The proof shows that opposite angles of a parallelogram are congruent. Given: ABCD is a parallelogram with diagonal AC. Prove: ∠ BAD ≅ ∠ DCB What is the missing reason In this partial proof? Question 3 options:
ASA Substution Angle Angle Postulate Alternate Interior Angles are Congruent
A parallelogram is a figure which has its opposite sides to be equal and parallel. The missing reason in the proof is:
B. Substitution Angle Angle Postulate.
A parallelogram is a type of quadrilateral that has its opposite sides to be equal and parallel. The sum of its internal angles is [tex]360^{o}[/tex].
To prove that ∠ BAD ≅ ∠ DCB, we have:
Given parallelogram ABCD;
<BAC ≅ <ACD (alternate angle theorem)
<DAC ≅ <ACB (alternate angle theorem)
<BAC + <DAC = <BAD
Also,
<BCA + <DCA = <BCD
Therefore,
<BAD ≅ <DCB (Substitution Angle Angle Postulate)
Thus, the missing reason in the partial proof is:
option B. Substitution Angle Angle Postulate
A sketch is attached to this question for more clarifications.
Visit: https://brainly.com/question/3100335
Help please just this whoever answers correctly I will mark brainliest
3. A library charges a late fee of $3.50 plus $0.15 per day that a book is returned late.
B. Make a table to find if the total fee if a book is 10,15,20, or 25 days late. Then graph the ordered pairs.
Answer: for question number 3 is 3.50+.15f
Step-by-step explanation:
Suchitra works at the local supermarket. She gets paid $22.50 per hour. Her time card
is shown below
Day In Out
Monday 9:00 a.m. 5:00 p.m.
Tuesday 9:00 a.m. 6:00 p.m.
Wednesday 8:30 a.m. 5:30 p.m.
Thursday 9:00 a.m. 4:30 p.m.
Friday 9:00 a.m. 4:00 p.m.
a How many hours did Suchitra work this week?
b .Find her weekly wage
Answer: she worked 31 hours ( I believe so)
Step-by-step explanation: hope that helps
For 250 points and brainiest......
Order the following number from least to greatest
1. -7, 0, -5
2. -3, -2, 10
3. -18.5, 18, -12.5
4. 26, -20, -24.5
Answer:
1.) -7,-5,0
2.)-3,-2,10
3.)-18.5,-12.5,18
4.)-24.5-20,26
Step-by-step explanation:
Here is the order
-7<-5<0#2
-3<-2<10#3
-18.5<-12.5<18#4
-24.5<-20<26For each ordered pair determine whether it is a solution to x=1
PLS HELP ASAP ILL GIVE BRAINLKEST THANKS
Answer:
w>-20
Step-by-step explanation:
30 points and brainliest answer asap pls
Answer:
ed - 7e = 4d + 3
ed - 4d = 3 + 7e
d( e - 4) = 3 + 7e
d = (3 + 7e)/( e - 4 )
100 POINTS Suppose ܶTU is on a coordinate plane located at T(-6,-2) and U(2,-6) Under a dilation of scale factor 1/4, TU becomes T'U' with coordinates T'(-3/2,-1/2) and U'(1/2,-3/2) Where is the center of the dilation located ?
A(0,0)
B(2,2)
C(4,0)
D(4,4)
c because the center of dilation is the multiplicatory value of the original point
I'm taking the ssat upper level on December 11th and really need help with the math section. Are there any tips or help that can be provided?
Answer:
1, Stay calm
2, be confident
3, if you know the type of questions they are gonna ask practiece those type of questions
Also good luck
It costs $22 to enter an amusement park and $0.50 to ride a ride. You have $23. Write an equation that represents the number r of rides you can ride.
Answer:
21.50 + 0.25r = 22.25
Step-by-step explanation:
Thats ur equationnn
How do you solve (x+4)2 ?
Answer:
Simplify the expression.
x2+8x+16
Step-by-step explanation:
I would like to know if somebody could help me on this math problem.
Answer:
$288
Step-by-step explanation:
.04 * 7,200= 288
Commission multiplied by Stocks sold= Answer
Hope this helps :)
Help me I don’t get this.
Answer:
i think its 105
Step-by-step explanation:
Help me guys!
Fill in the table using this function rule.
y = -2x+3
parallel perpendicular or neither
Answer:
parallel
Step-by-step explanation:
4-2/-9-0= 2/-9
6-8/4+5= -2/9
using the diagram what is the intersection of plane ABCD and GC
A. Plane EFGH
B. Point D
c. Point C
D. Line CB
Answer:
The answer it's c. Point C
What is the solution set of (x - 2)(x - 3) = 2?.
what is this question 9 + x to the power of 10
Answer:
ok im not sure but here is what i think the answer is
Step-by-step explanation:
answer 60466185
Hey everyone i would appreciate a step by step explanation. Also the actual question was written in mixed number form i just converted it into improper fractions.
10/9 + 56/27
Answer:
86/27 or 3 5/27
Step-by-step explanation:
10/9 is nothing but 30/27 (multiply the numerator and denominator by 3/3)
By adding 30/27+56/27, we get 86/27, which is our final answer
help please its 100 points if u get this right! ty have a nice day !
Answer:
6 mm²
Step-by-step explanation:
1/2 x 3 x 4 = Area of triangle
=> 2 x 3 = Area of triangle
=> 6 mm² = Area of triangle.
Hoped this helped.
Answer:
It's 15
Step-by-step explanation:
plz helpp what is b?
Answer:
41 degrees
Step-by-step explanation:
the two squares that make up the rhombus are both equilateral so we know that the measure of angle WUX is 56 degrees. subtract 15 from 56 and you get 41 degrees.
The humerus is the bone in a person's upper arm.With this bone as a clue,an anthropologist can tell about how tall a person was.If the bone belongs to that of a female,then height of the person is about (2.75 × humerus length)+71.48 cm .Supposed that the humerus of the female.Supposed that the humerus of a female was found to be 31cm long,about how tall was she? Show your solution
Nonsense=acc in brainly will be deleted
Answer:
156.73 cm
Step-by-step explanation:
height of the person = (2.75 × humerus length)+71.48 cm
length of the found humerus = 31cm
∴ height of the person = (2.75 × 31)+71.48 cm
= 85.25 + 71.48 cm
= 156.73 cm
GIVING BRAINLIEST!!!
A pole is being decorated with 15-meter ribbons that are strung from the top of the 7.2-meter pole to a point on the ground. Which is the approximate measure of the angle formed by the ribbon and the pole?
The angle formed by the ribbon and the pole is 29°
Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.
Let θ represent the angle formed by the ribbon and the pole.
Hence:
[tex]sin(\theta)=\frac{7.2}{15} \\\\\theta=sin^{-1}0.48\\\\\theta=29^o[/tex]
The angle formed by the ribbon and the pole is 29°
Find out more on Trigonometric ratio at: https://brainly.com/question/1201366
What is the quotient?
126 divided by 7
A. 18
B.16
C. 19
D. 17
Answer:
A
Step-by-step explanation:
I know that 20 times 7 is 140 and if I take away 2 sevens that leaves 126. So 126 \div 7 = 18
Answer:
A. 18
Step-by-step explanation:
I took a photo of my work I didn't know how I could type that here
Tell me if I'm wrong :)
What is the greatest common factor of 15, 35, and 10?
Answer: The GCF of 10, 15, and 35 is 5.
Would appreciate brainliest <3
Answer:
5.
Step-by-step explanation:
First, we write them in prime factor form, then pick out the common factors.
15 = 3*5
35 = 5*7
10 = 2*5
So the GCF is 5.
Is this answer right?
Answer:
yes
Step-by-step explanation:
Answer:
Your answer is correct! Good Job :)
Step-by-step explanation:
A bicycle store costs $1500 per month to operate. The store pays an average of $35 per bike. The average selling price of each bicycle is $85. How many bicycles must the store sell each month to break even?
Answer:
30 bikes
Step-by-step explanation:
the profit from each bike is 50 so then you divide 1500 by 50 and you get 30
3. A dish contains 100 candies. Juan removes candies from the dish each day and no
candies are added to the dish. On day 1, Juan removes 1 candy. On day 2, Juan
removes 2 candies. On each day that follows, Juan removes 1 more candy than he
removed on the previous day. After day n, Juan has removed a total of at least 64
candies. What is the smallest possible value of n?
Please give answers and how to solve it step by step thank you!!!
Answer:
11
Step-by-step explanation:
If i am correct n= the days so with the days adding up day 10 juan would have 55 of the 100 candies, day 11 he would have 66. The statement said at least 64, so it would have to be 64 or the closet amount to 64 but it cannot be lower than 64. So there for 66 is the closest to the given amount, and in order for juan to get 64 he would need to take candies out for 11 days.
solve the questions
Answer:
1
Step-by-step explanation:
= 21/21
= 1
Answer:
90
Step-by-step explanation:
let the number to be found be x then
23 [tex]\frac{1}{3}[/tex] % of x = 21 ( change mixed number to improper fraction )
[tex]\frac{\frac{70}{3} }{100}[/tex] x = 21
[tex]\frac{70}{300}[/tex] x = 21 ( multiply both sides by 300 to clear the fraction )
70x = 6300 ( divide both sides by 70 )
x = 90
Then 23 [tex]\frac{1}{3}[/tex] % 0f 90 = 21
rlly need help pls hurry fast
Answer:
Angles 7 and 8 are supplementary because they are a pair of adjacent angles that form a straight line.
Supplementary angles add up to 180°