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
1. 7.5 because Y/75 X 10/100 = 750 /100 = 7.5
2. .75 because Y/75 X 1/100 = 75/100 = .75
Answer:
697 marbles
Step-by-step explanation:
We know:
Briley- 374 marbles
Joey- 374*4
Carson- (374*4)-799
Solve:
374*4= 1496 (This is how many Joey has)
1496-799= 697 (This is how many Carson has)
Hope this helps!
Answer:
4 miles in 1 day
Step-by-step explanation: Multiply 8 by the numerator for how many miles of road; That is how many halves of miles are built in a single day. Simplify that and they build 4 miles of road a day.
2,5 * 10^3
25 * 10^2
0,25 * 10^4
