By using <span>De Moivre's theorem:
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If we have the complex number ⇒ z = a ( cos θ + i sin θ)
∴
![\sqrt[n]{z} = \sqrt[n]{a} \ (cos \ \frac{\theta + 360K}{n} + i \ sin \ \frac{\theta +360k}{n} )](https://tex.z-dn.net/?f=%20%5Csqrt%5Bn%5D%7Bz%7D%20%3D%20%20%5Csqrt%5Bn%5D%7Ba%7D%20%5C%20%28cos%20%5C%20%20%5Cfrac%7B%5Ctheta%20%2B%20360K%7D%7Bn%7D%20%2B%20i%20%5C%20sin%20%5C%20%5Cfrac%7B%5Ctheta%20%2B360k%7D%7Bn%7D%20%29)
k= 0, 1 , 2, ..... , (n-1)
For The given complex number <span>⇒ z = 81(cos(3π/8) + i sin(3π/8))
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Part (A) <span>
find the modulus for all of the fourth roots </span>
<span>∴ The modulus of the given complex number = l z l = 81
</span>
∴ The modulus of the fourth root =
![\sqrt[4]{z} = \sqrt[4]{81} = 3](https://tex.z-dn.net/?f=%20%5Csqrt%5B4%5D%7Bz%7D%20%3D%20%20%5Csqrt%5B4%5D%7B81%7D%20%3D%203)
Part (b) find the angle for each of the four roots
The angle of the given complex number =
There is four roots and the angle between each root =
The angle of the first root =
The angle of the second root =
The angle of the third root =
The angle of the fourth root =
Part (C): find all of the fourth roots of this
The first root =
The second root =
The third root =
The fourth root =
<h3>
Answer: Choice A. 82 websites per year</h3>
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How I got that answer:
We have gone from 54 websites to 793 websites. This is a change of 793-54 = 739 new websites. This is over a timespan of 2004-1995 = 9 years.
Since we have 739 new websites over the course of 9 years, this means the rate of change is 739/9 = 82.1111... where the '1's go on forever. Rounding to the nearest whole number gets us roughly 82 websites a year.
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You could use the slope formula to get the job done. This is because the slope represents the rise over run
slope = rise/run
The rise is how much the number of websites have gone up or down. The run is the amount of time that has passed by. So slope = rise/run = 739/9 = 82.111...
In a more written out way, the steps would be
slope = rise/run
slope = (y2-y1)/(x2-x1)
slope = (793 - 54)/(2004 - 1995)
slope = 739/9
slope = 82.111....
9514 1404 393
Answer:
(B) 4
Step-by-step explanation:
Consider the units column. The only sum of 3 and a single digit that will end in 1 is the sum ...
3 + 8 = 11
This tells you A = 8, so the top number is 1983, and the middle number is B78.
Considering the first two columns, we know that 83 +78 = 161, so there must be a carry of 1 into the third column. That makes it have the sum ...
1 + 9 + B = <something ending in 4>
We know the something cannot be 04 or 24, so must be 14. Then ...
10 + B = 14 ⇒ B = 4
__
So, the whole sum is ...
1983 +478 = 2461
and the letter values are ...
Answer:
540
Step-by-step explanation:
im terrible at explaining so-
Answer:
y = -2x - 10
Step-by-step explanation:
Slope intercept form of equation is of form
y = mx+c
where m is the slope of line and c is the y intercept of the line.
Y intercept is point on y axis where the line intersects the y axis.
_____________________________
Given equation
y = -2x +4
comparing it with y = mx+ c
m = -2 , c = 4
_____________________________
when two lines are parallel, their slopes are equal.
Let the equation of new line in slope intercept form be y = mx + c
Thus slope of of new required line is -2
Thus m for new line is -2.
now, equation of required line : y = -2x+c
Given that this line passes through (-4, -2). This point shall should satisfy equation y = -2x+c.
Substituting the value of (-4, -2) we have
-2 = -2(-4)+c
=> -2 = 8 +c
=> -2 -8 = c
=> c = -10.
Thus , equation of required line is y = -2x - 10.
