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
You have 32 tiles, you use 15 tiles, how many tiles are left?
You just went shopping with $32, you spent $15, how much money do you have left?
Your friend has 32 cards, he loses 15, how many cards does he have left?
Answer:
1. 322.01
Step-by-step explanation:
Formula: v=pi X r^2(h/3)
Answer with explanation:
The given mathematical expression to solve : 
The prime factorization of each term can be written as follows :-
We can see that the greatest common factor of both the terms = 
So we rewrite the given expression as :-
By using distributive property :-
, we have
