Answer:
6
Step-by-step explanation:
Answer:
Step-by-step explanation:
z₁ = 2 − 2i
z₂ = (1 − i) + √3(1 + i) = (1 + √3) + (√3 - 1) i
a) We get the modulus of z₁ as follows
║z₁║ = √((2)²+(-2)²) = 2
now we find the argument
α = Arctan (-2/2) = Arctan (-1) = -45º ⇒ α = 360º + (-45º) = 315º
b) z₁ = 2 Cis 315º
Although the complex number is in binomic or polar form, its representation must be the same, since the complex number is the same, only that it is expressed in two different forms. The modulus represents the distance from the origin to the point. The degree of rotation is the angle from the x-axis. When the polar form is expanded, the result is the rectangular form of a complex number.
c) If z₀*z₁ = z₂ and z₀ = a + b i
we have
(a + b i)*(2 − 2i) = (1 + √3) + (√3 - 1) i
⇒ 2a + 2bi - 2ai - 2bi² = (1 + √3) + (√3 - 1) i
⇒ 2a + 2bi - 2ai - 2b(-1) = (1 + √3) + (√3 - 1) i
⇒ 2a + 2b + 2bi - 2ai = (1 + √3) + (√3 - 1) i
⇒ 2 (a + b) + 2 (b - a) i = (1 + √3) + (√3 - 1) i
Now we can apply
2 (a + b) = 1 + √3
2 (b - a) = √3 - 1
Solving the system we get
a = 1/2
b = √3 / 2
Finally
z₀ = (1/2) + (√3 / 2) i
d) ║z₀║ = √((1/2)²+(√3 / 2)²) = 1
α = Arctan ((√3 / 2)/(1/2)) = 60º
e) z₀ = Cis 60º
f) Since z₂ = z₀*z₁, then z₂ is the transformation of z₁ rotated counterclockwise by arg(w) which is 60º
Answer:
(1)
x = 128/3
y = 52/3
(2)
x=3
Step-by-step explanation:
(1)
x+y=60 => 3y=52 => y=52/3 => x=128/3
x=2y+8
(2)
M1V1 + M2V2 = MV
x × 10 + x × 70 = 6 × 40
80x = 240
x = 3
This equation is written in point-slope form.
In this equation we have the point (2, 12) and the slope of 4.
Slope-intercept form: y = mx + b
m = slope
b = y-intercept
Use the point (2, 12) to solve.
12 = 4(2) + b
12 = 8 + b
12 - 8 = 8 + b - 8
4 = b (y-intercept)
Hope This Helped! Good Luck!
Answer:
600ft
Step-by-step explanation:
The balloon falls 200 feet in one minute and we need the amount it fell in 3 minutes: 200feet*3minutes = 600 ft
