Hi, I am new to this website :) I'm currently taking an online trig class on De Moivre's theorem and I don't understand it at al
l! The question is: Write each expression in the standard form for a complex number, a+bi. 1. [3cos(27))+isin(27)]^5
2. [2(cos(40))+isin(40)]^6
any info regarding this question would be extremely helpful! Thanks!
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)
The perimeter of the large square is 24 and the area is 36 units the perimeter of the small squares are 4 and the areas are 1 unit. All together the perimeter is 29 and the area is 38.
