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)
Part A) Find BC, the distance from Tower 2 to the plane, to the nearest foot.
in the triangle ACD
sin16=CD/(7600+BD)--------> CD=sin16*(7600+BD)---------> equation 1
in the triangle BCD
sin24=CD/BD-----------> CD=sin24*BD---------------> equation 2
equation 1=equation 2
sin16*(7600+BD)=sin24*BD-----> sin16*7600+sin16*BD=sin24*BD
sin24*BD-sin16*BD=sin16*7600----> BD=[sin16*7600]/[sin24-sin16]
BD=15979 ft
in the triangle BCD
cos24=BD/BC---------> BC=BD/cos24-------> 15979/cos24-------> 17491
BC=17491 ft
the answer part 1) BC is 17491 ft
Part 2) Find CD, the height of the plane from the ground, to the nearest foot.
CD=sin24*BD ( remember equation 2)
BD=15979 ft
CD=sin24*15979 -----------> CD=6499 ft
the answer part 2) CD is 6499 ft
Hi there!
To solve this problem, we need to simplify.
2/3x = 12
To isolate x, we should multiply both sides of the equation by the reciprocal of 2/3 to make x equal to a value:
Reciprocal of 2/3 = 3/2
x = 12 * 3/2
x = 18
Hope this helps!