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:
Step-by-step explanation:
First you want to understand that every time a radio wave goes 300,000,000 meters a second passes, literally what meter per second means. of course it doesn't go that far, it goes 384,000 one way and then the same distance back, which makes 768,000. Under a third of the distance to make 1 second, so it will be less than one second.
You also want to understand the formula for speed. speed = distance / time. Whch also means, to find time you can change it to be time = distance / speed. And hey, we have distance and speed. 768,000 / 300,000,000 = .00256, I'll leave the significant figures to you unless you need help with them. but that's .00256 of a second. or .00256 s
M = -1/2
B = 1
Equation shown is y = mx + b
Answer:
Step-by-step explanation:
y = f(x)
y = 2x+3
You need to switch the places of x and y, into this:
x = 2y + 3
Then solve for y:
2y = x-3
Answer:
You would be able to go 165 miles in total
Step-by-step explanation:
You are going 60 miles per hour, so that instantly brings you up to 120 miles, because you are there for 2 hours and 45 minutes. Because you are going exactly 60 mph, and each hour is 60 minutes, you can compare that you go 1 mile per minute. If this statement is true, you'll go another 45 miles, bringing you to a grand total of 165 miles.
