De Moivre's theorem uses this general formula z = r(cos α + i<span> sin α) that is where we can have the form a + bi. If the given is raised to a certain number, then the r is raised to the same number while the angles are being multiplied by that number.
For 1) </span>[3cos(27))+isin(27)]^5 we first apply the concept I mentioned above where it becomes
[3^5cos(27*5))+isin(27*5)] and then after simplifying we get, [243 (cos (135) + isin (135))]
it is then further simplified to 243 (-1/ √2) + 243i (1/√2) = -243/√2 + 243/<span>√2 i
and that is the answer.
For 2) </span>[2(cos(40))+isin(40)]^6, we apply the same steps in 1)
[2^6(cos(40*6))+isin(40*6)],
[64(cos(240))+isin(240)] = 64 (-1/2) + 64i (-√3 /2)
And the answer is -32 -32 √3 i
Summary:
1) -243/√2 + 243/√2 i
2)-32 -32 √3 i
A) His estimate is incorrect, since he has increased a figure to the amount that each employee would receive.
B) Rounded to the nearest dollar, each employee would receive $ 209.
Since a company has $ 6582 to give out in bonuses, and an amount is to be given out equally to each of the 32 employees, and A) a manager, Jake reasoned that since 32 goes into 64 twice, each employee will get about $ 2000 , to determine if his estimate is correct, and B) determine how much will each employee receive, rounded to the nearest whole dollar, the following calculations must be performed:
A)
- 2000 x 32 = 64000
- 200 x 32 = 6400
Therefore, his estimate is incorrect, since he has increased a figure to the amount that each employee would receive.
B)
Therefore, rounded to the nearest dollar, each employee would receive $ 209.
Learn more about maths in brainly.com/question/8865479
Step-by-step explanation:
Assume that
hence,
now,
attached below is the complete solution
Answer:
Simplest polynomial: x²+x-12
Step-by-step explanation:
zeroes of polynomial= 3,-4
Therefore,
f(3) =0
f(-4)=0.
By factor Theorem
(x-3) and (x+4) are factors
so simplest polynomial is
(x-3)(x+4)
= x² - 3x + 4x -12
= x² + x -12
.
Hope it helps
