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:
(98+89+88+x)/5 > 92
366+x/ 5 > 92
x/5 + 73.2 > 92
x/5 > 18.8
x > 94
The lowest score that you can make and have a 92 average is a 94. Hope this helps!
Step-by-step explanation:
Answer:
$27
Step-by-step explanation:
Set up a proportion where x is the amount of money he saved:
= 
Cross multiply and solve for x:
12x = 324
x = 27
So, he saved $27
Answer:
b. {x l -9/7 < x <17/7}
Step-by-step explanation:
l 4 - 7xl -5 < 8
Adding 5 on both sides, we get
l4 - 7xl < 13
Absolute function has two values.
{ 4 - 7x < 13 and (4-7x) > -13}
Now let's solve for x.
-7x < 9 and -7x > -17
x > -9/7 and x < 17/7
Now we have to combine the two inequalities and write the solution
{x l -9/7 < x <17/7}
Answer: b. {x l -9/7 < x <17/7}
Hope this will helpful.
Thank you.
