Answer:
Step-by-step explanation:
The genral form of a complex number in rectangular plane is expressed as z = x+iy
In polar coordinate, z =rcos ∅+irsin∅ where;
r is the modulus = √x²+y²
∅ is teh argument = arctan y/x
Given thr complex number z = 6+6√(3)i
r = √6²+(6√3)²
r = √36+108
r = √144
r = 12
∅ = arctan 6√3/6
∅ = arctan √3
∅ = 60°
In polar form, z = 12(cos60°+isin60°)
z = 12(cosπ/3+isinπ/3)
To get the fourth root of the equation, we will use the de moivres theorem; zⁿ = rⁿ(cosn∅+isinn∅)
z^1/4 = 12^1/4(cosπ/12+isinπ/12)
When n = 1;
z1 = 12^1/4(cosπ/3+isinn/3)
z1 = 12^1/4cis(π/3)
when n = 2;
z2 = 12^1/4(cos2π/3+isin2π/3)
z2 = 12^1/4cis(2π/3)
when n = 3;
z2 = 12^1/4(cosπ+isinπ)
z2 = 12^1/4cis(π)
when n = 4;
z2 = 12^1/4(cos4π/3+isin4π/3)
z2 = 12^1/4cis(4π/3)
Answer:
It's D
Step-by-step explanation:
I can't see the option D
But, A,B, and C are absolutely incorrect.
Answer:
(x - 5)² = 41
Step-by-step explanation:
* Lets revise the completing square form
- the form x² ± bx + c is a completing square if it can be put in the form
(x ± h)² , where b = 2h and c = h²
# The completing square is x² ± bx + c = (x ± h)²
# Remember c must be positive because it is = h²
* Lets use this form to solve the problem
∵ x² - 10x = 16
- Lets equate 2h by -10
∵ 2h = -10 ⇒ divide both sides by 2
∴ h = -5
∴ h² = (-5)² = 25
∵ c = h²
∴ c = 25
- The completing square is x² - 10x + 25
∵ The equation is x² - 10x = 16
- We will add 25 and subtract 25 to the equation to make the
completing square without change the terms of the equation
∴ x² - 10x + 25 - 25 = 16
∴ (x² - 10x + 25) - 25 = 16 ⇒ add 25 to both sides
∴ (x² - 10x + 25) = 41
* Use the rule of the completing square above
- Let (x² - 10x + 25) = (x - 5)²
∴ (x - 5)² = 41
It means that two people are friends, like two peas in a pod
Answer:
It takes four hours because the little bro is alone and only one lawn mower is used
