Well 21 times 2 is 42 and 1/3 of 21 is 7 so 42+7 is 49. hope this is right
The mean of the problem is 37.3. All you need to do is add all the numbers together and then divide them by the amount of numbers. So I added them all and divided by 10.
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
Well Those are variables and it is using the Distributive property to solve. For example P(a+b) simplify P*a + P*b.
Look at the picture.
The base of the ladder is 6.47 feet from the house.
