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:
40
Step-by-step explanation:
why? because 40x40=1600
Answer:
1/3 you will add it to get your main description and get your final answer
If you were at 54 on the number line you would have to cross zero and go an extra 13 steps to get to -13.
So we want the difference between 54 and -13 or 54- -13 which becomes 54+13 which is 67 - that is the range
3/16 as a decimal is 0.18
and 5/48 as a decimal is 0.10
SO
you have 0.10, 0.18, 0.75, and 0.5 so put that in order
