Answer:
The answer is 
Step-by-step explanation:
Answer:
4.24
Step-by-step explanation:
Answer: $506.25
Step-by-step explanation:
1. Find 40% of $843.75
- The decimal value of 40% is 0.4. We can multiply 0.4 by 843.75 to find the discount on the computer.
-> 0.4*843.75= 337.5
2. Now that we have the discount, we can subtract 40% of the original price to find the new price.
843.75 - 337.5 = $506.25
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
