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
Simplifying
P + -21 + -21 = 34 + -21
-21 + -21 + P = 34 + -21
Combine like terms: -21 + -21 = -42
-42 + P = 34 + -21
Combine like terms: 34 + -21 = 13
-42 + P = 13
Solving
-42 + P = 13
Solving for variable 'P'.
Move all terms containing P to the left, all other terms to the right.
Add '42' to each side of the equation.
-42 + 42 + P = 13 + 42
Combine like terms: -42 + 42 = 0
0 + P = 13 + 42
P = 13 + 42
Combine like terms: 13 + 42 = 55
P = 55
Simplifying
P = 55
I put the solution on the paper
Lisa gave her sister 1/4, or one-fourth of her toy cars. Brainliest would really help!
