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
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ2
Let l be the length of a diagonal of a rectangle whose sides have lengths x and y, and assume that x and y vary with time. If x increases at a constant rate of 19 ft/s and y decreases at a constant rate of 15 ft/s, how fast is the size of the diagonal changing when x
The rate of change of the size of the diagonal is; 25.2 ft/s
By Pythagoras theorem;
The length, l of a diagonal of a rectangle whose sides have lengths x and y is;
l² = x² + y².In essence; the length of the diagonal is dependent on the length, x and y of the sides.
Therefore;
(dl/dt)² = (dx/dt)² + (dy/dt)²
where;
(dx/dt) = 19 ft/s(dy/dt) = -15 ft/sTherefore,
(dl/dt)² = 19² + (-15)²
(dl/dt)² = 361 + 225
dl/dt = √586
dl/dt = 25.2
Therefore, the size of the diagonal is changing at a rate of; 25.2 ft/s.
Read more;
https://brainly.com/question/12559989
pls help asap MIDSEGMENTS
Answer:
tttttttttttttttttttttttttttttttttttttttttttttt
You can buy a seat cushion at the College Softball World Series for $4. They
paid $2.50 to have them made, and they make a profit of $300 when sold out.
How many seat cushions did they have made?
Answer:
$118.40
2.50x Plus 4 Equal 300
2.50x Equal 296
2.50x/2.50 Equal $118.40
PLEASE TELL ME IF I AM WRONG!WILL GIVE LOTS OF POINTS HELP SOLVE SOON, NUMBER 7
Answer: 4x + 3 = 39
Step-by-step explanation:
Because you don't know how much each pizza costs, you can write it as x.
You multiply x by 4 to get 4x and add 3 because thats how much the chips cost.
That added up should equal 39 because thats how much he spent.
Answer: The answer is C ( 4x + 3 = 39 )
Step-by-step explanation:
4 = number of Pizzas. x = price of pizza. 3 = price of chips. 39 = total of 4 pizzas and chips together.
1) 4x + 3 = 39
2) 4x = 39 - 3
You will seperate the variable(4x) and the constants(3 and 9) So, you move (+3) to the other side making it negative. Then, you subtract (39-3) which will equal to (36)
4) 4x = 36
5) x = 36/4
You want to move the coefficient(4) to the other side. Thus, will make it a division becaue the oppisite of multiplication is division. So you cancel it out from x because 4/4 is 1.
6) x = 9
You divided 36/4 which will equal to 9
7) 4(9) + 3 = 39
what is the solution of the equation w^2=4/9? show work.
Answer:
w = ± [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
w² = [tex]\frac{4}{9}[/tex] ( take square root of both sides )
w = ± [tex]\sqrt{\frac{4}{9} }[/tex] = ± [tex]\frac{\sqrt{4} }{\sqrt{9} }[/tex] = ± [tex]\frac{2}{3}[/tex]
Then
w = - [tex]\frac{2}{3}[/tex] or w = [tex]\frac{2}{3}[/tex]
simplify √ 18 + √ 20 - √ 45
Answer:
3√2 - 4√5 -
ig this is the answer
Answer:
3[tex]\sqrt{2}[/tex] - [tex]\sqrt{5}[/tex]
Step-by-step explanation:
Using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]
Simplifying the radicals
[tex]\sqrt{18}[/tex]
= [tex]\sqrt{9(2)}[/tex]
= [tex]\sqrt{9}[/tex] × [tex]\sqrt{2}[/tex]
= 3[tex]\sqrt{2}[/tex]
---------------------------
[tex]\sqrt{20}[/tex]
= [tex]\sqrt{4(5)}[/tex]
= [tex]\sqrt{4}[/tex] × [tex]\sqrt{5}[/tex]
= 2[tex]\sqrt{5}[/tex]
------------------------
[tex]\sqrt{45}[/tex]
= [tex]\sqrt{9(5)}[/tex]
= [tex]\sqrt{9}[/tex] × [tex]\sqrt{5}[/tex]
= 3[tex]\sqrt{5}[/tex]
Then
[tex]\sqrt{18}[/tex] + [tex]\sqrt{20}[/tex] - [tex]\sqrt{45}[/tex]
= 3[tex]\sqrt{2}[/tex] + 2[tex]\sqrt{5}[/tex] - 3[tex]\sqrt{5}[/tex] ← collect like terms
= 3[tex]\sqrt{2}[/tex] - [tex]\sqrt{5}[/tex]
Which expression shows the distance on the number line between −3 and −10 ?
Answer:
D. |-3 - (-10)|
Step-by-step explanation:
Finding slopes. Please do as many questions as you can.
Answer:
Step-by-step explanation:
slope are hard tbh
make y the subject of each of y-p=m
Answer:
y=m+p
Step-by-step explanation:
take the p to the other side.
p crosses = sighn and becomes +
hence ans = y=m+ p
Jane’s bank account grew from $2175 to $2262. What was the percent increase in her account?
Answer:
I believe it increased by 10%
Step-by-step explanation:
x^3 - 3x^2 + 4x - 12
Answer:
(x^2 + 4)(x - 3).
Step-by-step explanation:
I'm guessing you want to factor this.
You can do it by grouping:
x^3 - 3x^2 + 4x - 12
= x^2(x - 3) + 4(x - 3)
= (x^2 + 4)(x - 3).
（︶^︶）Brainliest for everyone!!!! ohh wait ????
Answer:
[tex]\frac{81}{256}[/tex]
Step-by-step explanation:
[tex](\frac{3}{4})^4 \\\rule{150}{0.5}\\\\\text{Note the exponent rule: }( \frac{a}{b}) ^c = \frac{a^c}{b^c} \\\rule{150}{0.5}\\\\\frac{3^4}{4^4}\\\\\rightarrow 3^4 = 81\\\rightarrow 4^4 = 256\\\\\boxed{\frac{81}{256}}\\\\\text{The answer is already in it's simplest form.}[/tex]
5.f(1)+5.g(9)=
Please answer the questions
Answer:
5f+45g
Step-by-step explanation:
Simplify
5*f(1) = 5f
5*g(9) = 45g
5f+45g
The ratio of students in Class X to Class Y is 2 : 5. There are 24 more students in Class Y than Class X. How many students must transfer from Class Y to Class X so that both classes have equal number of students?
Answer: 12 students
Step-by-step explanation:
Let X and Y stand for the number of students in each respective class.
We know:
X/Y = 2/5, and
Y = X+24
We want to find the number of students, x, that when transferred from Y to X, will make the classes equal in size. We can express this as:
(Y-x)/(X+x) = 1
---
We can rearrange X/Y = 2/5 to:
X = 2Y/5
The use this value of X in the second equation:
Y = X+24
Y =2Y/5+24
5Y = 2Y + 120
3Y = 120
Y = 40
Since Y = X+24
40 = X + 24
X = 16
--
Now we want x, the number of students transferring from Class Y to Class X, to be a value such that X = Y:
(Y-x)=(X+x)
(40-x)=(16+x)
24 = 2x
x = 12
12 students must transfer to the more difficult, very early morning, class.
PLS HELP ASAP ITS FOR MY ASSIGNMENT DUE RN!!! WHOEVER ANSWERS FIRST GETS BRAINLIEST, 5 STARS, AND A THANKS!!!!
[tex]\\ \sf\longmapsto 9\dfrac{7}{11}-(5+1\dfrac{1}{2})[/tex]
[tex]\\ \sf\longmapsto4 \dfrac{7}{11}-1\dfrac{1}{2}[/tex]
[tex]\\ \sf\longmapsto 4\dfrac{14}{22}-1\dfrac{11}{22}[/tex]
[tex]\\ \sf\longmapsto 3\dfrac{3}{22}[/tex]
Write an algebraic expression to represent the verbal statement: The product of the difference of m and 7 and 6.
Answer:
(m-7) * 6
Step-by-step explanation:
you follow the statement from left to right. You see that there's a product so you write a product sign
*
then you know its the difference of m-7 on one side and 6 on the other getting
(m-7) * 6
What is it called when heat and pressure change one type of rock into another? (100 points)
a metamorphism
b erosion
c deposition
d crystallization
Answer:
A: metamorphic
Step-by-step explanation:
Answer:
it's a
Step-by-step explanation:
I read it in a textbook
Write two expressions for the perimeter of the figure.
Answer:
(a) 5 + 7 + 6x + 8x + 6
(b) 18 + 14x
Step-by-step explanation:
What are the names of these polygons?
a)
b)
c)
d)
can anyone help pls?
Please help! 20 points! Will give brainliest!
Answer:
2 and 4 are correct
Step-by-step explanation:
Hope this helps!❄︎
I need some help please. I don't understand this. :)
Answer:
i dont know sorry
Step-by-step explanation:
pls ask someone else thanks have a nice day
What is the surface area of the cylinder with height 7 cm and radius 5 cm? Round
your answer to the nearest thousandth.
Answer:
376.991 cm²
Step-by-step explanation:
[tex]SA_{cylinder} = 2\pi r^{2} + 2\pi rh[/tex]
Surface Area = 2π(5²) + 2π(5)(7)
= 50π + 70π
= 120π
= 376.9911184... ≈ 376.991
Derive Surface Area of A CylinderIf you take a look at a net of a cylinder, you can see it is composed of two circles(bases) and a rectangular strip with the length of the diameter of the circle
The formula for the area of a circle = πr², and since there are 2, it is 2πr²
The formula for circumference of a circle = 2πr, and since we are multiplying that by the height by the height of the cylinder, it is 2πrh
∴ 2πr² + 2πrh
Create and solve a problem involving the number 7.52 million that would require you to divide.
Answer:
7.52 million divided by 1
Step-by-step explanation:
Find the term-to-term rule of this sequence:5,6,8,12
Answer:
5,6,8,12,20,36,68
please answer this for me!!
Answer:
x = 40
y = 8
Step-by-step explanation:
3x-9 = 2x+31
3x-2x = 31+9
x = 40
4y+5 = 2y+21
4y-2y = 21-5
2y=16
y=8
What is an equation of the line that passes through the points (6, 2)and (-6, -8)
Answer:
Step-by-step explanation:
(-8 - 2)/(-6 - 6)= -10/-12= 5/6
y - 2 = 5/6(x - 6)
y - 2 = 5/6x - 5
y = 5/6x - 3
for a brainlist pls answer
Find the intercepts of the given equation. To earn full credit, show your work using a method explained in the Orientation.
Answer:
[tex]x=-2y+10[/tex]
Step-by-step explanation:
Step 1: Flip the equation.
Step 2: Add -5 to both sides.
Step 3: Divide both sides by (-1)/2.
Which of the following could be the measure of the angle below
Answer:
-180
Step-by-step explanation:
its a straight line
A pot contains 3 1/3 cups of oatmeal.
How many 3/5 cup servings is this? How much will be left
Answer:
2 11/15
Step-by-step explanation:
Hope this helps please mark brainliest if I helped! Thanks
Solve the equation: (5y + 2)(y - 3) = -13(2 + y)
Answer:
2i
Step-by-step explanation:
Distribute:
(5y + 2)(y - 3)
5y^2-15y+2y-6
Which can be simplified into 5y^2-13y-6
Now the equation now looks like this: 5y^2-13y-6=-13(2+y)
For -13(2+y) multiply -13 with 2+y
Which is -26-13y
5y^2-13y-6=-26-13y
Simplify:
5y^2+20
Which can be simplified into 5(y^2+4)
y^2+4=0
y^2=-4
y=2i
Hope this helps!