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:
Step-by-step explanation:
- <em>Percent change is the difference in numbers divided by initial number converted to percent value.</em>
<u>Percent increase:</u>
<u>Percent decrease:</u>
- (70 - 50)/70*100% = 28.57%
<u>Compare:</u>
Answer:
a? sorry if it wrong
Step-by-step explanation:
