Answers
Answer:
The square roots of 49·i in ascending order are;
1) -7·(cos(45°) + i·sin(45°))
2) 7·(cos(45°) + i·sin(45°))
Step-by-step explanation:
The square root of complex numbers 49·i is found as follows;
x + y·i = r·(cosθ + i·sinθ)
Where;
r = √(x² + y²)
θ = arctan(y/x)
Therefore;
49·i = 0 + 49·i
Therefore, we have;
r = √(0² + 49²) = 49
θ = arctan(49/0) → 90°
Therefore, we have;
49·i = 49·(cos(90°) + i·sin(90°)
By De Moivre's formula, we have;
[tex]r \cdot (cos(\theta) + i \cdot sin(\theta) )^{\dfrac{1}{2}} = \pm \sqrt{r} \cdot \left (cos\left (\dfrac{\theta}{2} \right ) + i \cdot sin\left (\dfrac{\theta}{2} \right ) \right )[/tex]
Therefore;
√(49·i) = √(49·(cos(90°) + i·sin(90°)) = ± √49·(cos(90°/2) + i·sin(90°/2))
∴ √(49·i) = ± √49·(cos(90°/2) + i·sin(90°/2)) = ± 7·(cos(45°) + i·sin(45°))
√(49·i) = ± 7·(cos(45°) + i·sin(45°))
The square roots of 49·i in ascending order are;
√(49·i) = - 7·(cos(45°) + i·sin(45°)) and 7·(cos(45°) + i·sin(45°))
Related Questions
Jim paid a gym membership fee of $50, plus $20 per month. Jim has paid a total of $290 to thegym. Which equation matches this situation?
Answers
Answer:
50+20x=290 or 50+(20x12)=290
Step-by-step explanation:
Answer:
50 + 20m = 290
Step-by-step explanation:
The answer is 50 + 20m = 290, because Jim paid a membership fee that was $50. Then each month he paid $20 because of his new membership. Jim never paid $50 a month, that was only his starter fee, but then gradually paid $20 every month so it would be 20m. Hope this helped.
Which answer is correct??
Answers
Answer:
8
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
y
2
−3=1
1
2
y+−3=1
1
2
y−3=1
Step 2: Add 3 to both sides.
1
2
y−3+3=1+3
1
2
y=4
Step 3: Multiply both sides by 2.
2*(
1
2
y)=(2)*(4)
y=8
Answer:
C.
Step-by-step explanation:
Replace y with each value.
If y is 2 then the answer would be -2
If y is 4 then the answer would be -1
If y is 8:
8/2 = 4
4-3 = 1
Please mark brainliest if this answer helped.
Happy Learning!
Simplify (2x-9)(4x+1)
Answers
Answer:
the answer is 8x^2-34x-9
Answer:
8x^2 - 34x - 9
Step-by-step explanation:
Can someone please help me with math.
Answers
Answer:
c
Step-by-step explanation:
c
A store pays $147 for a skateboard. If the store marks it up 75%, then marks it down 22%. What is the new cost
Answers
Answer:
$200.65
Step-by-step explanation:
If they bought it for 147 then marked it up 75% you would do
$147+75% = 257.25
THEN they mark down
257.25 - 22% = $200.255 which would be
$200.25 orrr $200.26
:) ur thoughts on this???
Answers
Answer:
it looks dead ..............
Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
with what??!!
Step-by-step explanation:
Answer:
This is essay thank you
Step-by-step explanation:
Can someone please help me with this math problem please:):)
Answers
Answer:
y = 126° + 29° = 155°
Step-by-step explanation:
I think this may be a solution:
126°+29°=155°
So, y=155°
Tell whether the line or segment is the best described as a chord,a diameterdiameter,or a raduis of a circle
Answers
Answer:
37
Step-by-step explanation:
rewrite the equation 12x=13-x^2
Answers
Answer:
x^2+12x-13 = 0
Step-by-step explanation:
12x=13-x^2
=>12x+x^2=13-x^2+x^2
=>x^2+12x-13 = 13-13
=> x^2+12x-13 = 0
Answer:
x² + 12x - 13 = 0
Step-by-step explanation:
12x = 13 - x²
the standard form of an equation is written starting from the variable of the highest degree to the lowest. Hence after rearranging;
0 = 13 - x² - 12x
0 = -x² - 12x + 13
In an equation, the highest degree of a variable should preferably be postive hence the equation to the left side to remove the negative sign:
x² + 12x - 13 = 0
How many more brooms must each earn in order to have enough credit to get a month off with pay?
Answers
Answer:
5
Step-by-step explanation:
Are both of theses sets of orderd pairs a function? {(4,2) (3,15) (2,18) (1,21)} {(-6,8) (-3,4) (3,0) (6,-4)
Answers
Answer:
yes!
Step-by-step explanation:
Ryan's take-home pay is $2,500 each month. The amount for gas is $125. Calculate the percentage Ryan uses on gas from his take-home pay. please help!! O^O
Answers
Answer: 5%
Step-by-step explanation:
Since Ryan's take-home pay is $2,500 each month and the amount for gas is $125.
The percentage that Ryan uses on gas from his take-home pay will be:
= Amount used on gas / Take home pay × 100
= 125/2500 × 100
= 1/20 × 100
= 5%
He used 5% on gas.
Which expression shows 3 decreased by the sum of 11 and a number? A. 3-(11+x) B. (11+x)-3 C. 3-11+x D. 3+11x
Answers
Answer:A
Step-by-step explanation:
Answer:
The correct answer Its A. 3-(11+x)
Help me pless!!!!!!!!!
Answers
Answer:
p = 7
Step-by-step explanation:
2p = 14
p = 14/2
p = 7
Write an equation for the line parallel to the given line that contains C.
C(1,4); y=−3x+1
Answers
Answer:The equation of a line is y = mx + b where y = y-coordinate, m = slope, x = x-coordinate, and b = y-intercept. (Remember that the slope is the steepness of a line and the y-intercept is the point where the line intersects the y-axis. The x- and y-coordinates are values of the points on the line of y = 3x - 1.)
Step-by-step explanation:
louise decided to purchase a new mountain bike when he saw the sporting good store was offering 20% off their bike. what is the total cost of the mountain bike if the originally price at $249 and louise must pay 7.5% sales tax
Answers
First off $249 x 20% = $49.8 so, $249- 49.8 = 199.2 ( the price after deducting the discount), 199.2 x 8% = 15.93 (this is the price of the tax), and 199.2 + 15.93 = $215.13 ( this is the price after the discount and with taxes) :D
Find the measure of AC
Answers
Answer:
7 inch
Step-by-step explanation:
AC= BC+AB
= (BD-CD) + radius of B
= (radius of B-radius of D) + 4.5
=(4.5-2) +4.5
=2.5+ 4.5
=7 inch
I hope this is correct.
How do you do √1/3/5
Answers
Answer:
Write
1
as a fraction with a common denominator.
−
√
5
5
−
3
5
Combine the numerators over the common denominator.
−
√
5
−
3
5
Subtract
3
from
5
.
−
√
2
5
Rewrite
√
2
5
as
√
2
√
5
.
−
√
2
√
5
Multiply
√
2
√
5
by
√
5
√
5
.
−
(
√
2
√
5
⋅
√
5
√
5
)
Combine and simplify the denominator.
Tap for more steps...
−
√
2
√
5
5
Simplify the numerator.
Tap for more steps...
−
√
10
5
The result can be shown in multiple forms.
Exact Form:
−
√
10
5
Decimal Form:
−
0.63245553
…
()|[]√≥°
789≤θ
456
In the right triangle shown, m\angle Y = 30\degreem∠Y=30°m, angle, Y, equals, 30, degree and XY= 6XY=6X, Y, equals, 6.
Answers
Answer:
YZ = 6.93
Step-by-step explanation:
Find the complete question attached
From the diagram, we are to look for YZ
Given the following
XY = adjacent = 6
measure of m<Y = 30degrees
Required
YZ = hypotenuse
Using the SOH CAH TOA identity
Cos theta = adjacent/hypotenuse
Cos 30 = XY/YZ
Cos 30 = 6/x
x = 6/cos30
x = 6/0.8660
x = 6.93
Hence the length of YZ is 6.93
Polly has 2 1/2 cups of cereal. How many 3/4 cup full servings can she make? Will she have any cereal left?
Answers
Answer:
She can make 3 cups of it with 1/3 of a cup leftover.
Step-by-step explanation:
2 1/2 = 5/2
5/2 ÷ 3/4
5/2 · 4/3
10/3
3.33
Layna can paint a 350-square foot room in 4 hours. It takes Bebe 7 hours to paint the same room. Which equation can be used to find the time in hours, t, it takes Layna and Bebe to paint the room together?
Answers
I am 99% sure this is correct. Good luck
Answer:
A. 1/4t+1/7t=1
Step-by-step explanation:
Please help I’ll mark brainliest
Answers
Answer:
y= x-3
Step-by-step explanation:
use the slope formula which is y= m(slope)x + b(y intercept)
The slope is one, so you can just leave it as x, and the y intercept is -3 so you can plus that into the b.
Hope this helps :)
165 x 0.38² to two decimal place
Answers
Answer:
23.83
Step-by-step explanation:
can someone please help me with this?
Answers
Y=250+10c
The 250 is the b and the 10c is the mx
Find the sum of 6x2 – 1 and x + 9.
Answers
Please find the attached photograph for your answer.
PLEASE HELP THANK YOU
Answers
Answer:
thanks you too for having us
based on the table, what is the slope,m, and y-intercept , b , on the line that models this relationship?
Answers
Answer: slope: 180 y intercept: -360
I hope this helps!
Eric carved this solid out of wood.
Find the volume of the solid
Answers
Answer:
3,456
Step-by-step explanation:
Just did the question and got it correct.
Hope this helps ;)
what is the value of x? 26 degrees tangent lines
Answers
Answer:
154°Step-by-step explanation:
The central angle and the angle between the tangents are supplementary, so
x + 26° = 180° ( subtract 26° from both sides )
26 - 26 = 0
180 - 26 = 154
x = 154°
The value of the x will be 154°.
How to find the interior central angle?The central angle and the angle between the tangents are supplementary.
If there is a circle O with tangent line L intersecting the circle at point A, then the radius OA is perpendicular to line L.
So,
x + 26° = 180°
Subtract 26° from both sides;
x + 26 - 26 = 180 - 26
x = 154°
Hence, the value of the x will be 154°.
Learn more about tangents ;
https://brainly.com/question/10024457
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