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
Answer:
y = 2.5 + 4.75, every additional rose sold , x, increases the cost of the rose, y, by 2.50
Step-by-step explanation:
Answer:
34 rolls
Step-by-step explanation:
For Frank to cover his whole ceiling, he needs paper that will cover
20 ft x 20 ft
20 x 20 = 400 ft
So, Frank needs to cover 400 ft of the ceiling. He has to split up this large need for paper into smaller rolls, because the rolls he can buy are small.
If each roll has 12 ft, we need to find how many 12-feet are in 400 feet.
To do this, we should divide
400 / 12
= 33.333
Because Frank cannot cover the whole ceiling using only 33 rolls, he has to buy an additional roll to make sure he can cover the extra area [that would be left over if he were to only buy 33 rolls, which would only cover 396 feet]
So, Frank will need to buy 34 rolls to have enough paper to entirely cover his ceiling.
Answer:B is the answer for this question
Answer:
J, K, and L
Explanation:
It needs to be a flat surface to be the same coplanar the only answer that is flat is J, K, and L
