Step-by-step explanation:
our equation is x²+16x = -44
- x²+16x= -44
- x² is the first term so weill have in the middle 2*x* a number
- x²+2*x*8 = -44
- the third term is 8² wich is 64 so we will add it in both sides
- x²+2*x*8+64 = -44+64
- (x+8)² = 20
Now that we have completed the perfect square let's solve the equation
- (x+8)² = 20
- x+8 =
or x+8= - - x = -8+ or x = -8-
so the first answer is the correct one
64; 8 +/-
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
