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:
4592.7
Step-by-step explanation:
Add them up:
4000 + 500 + 90 + 2 + 0.7 = 4592.7
(x + 1)·(x + 1 + 11) = (x + 4)·(x + 4 + 1) --> x = 2
Tools like "photomath" are able to help you solving such equations.
Answer:
The circumference of a circle is the distance around the entire circle, while arc length, s, is the distance <u>between</u> two points on the circle.
C = 2πr = 2π( <u>5</u><u> </u>) = 10π ≈ 31.4 units
3.14 is an approximation for π.
s = θ/360° (C)
mAB = 60°/360° ( 31.4)
= <u>1</u><u>/</u><u>6</u>(31.4) ≈5.2 units
Answer: equilateral
Step-by-step explanation:
