There are two answers to this question
the first possible answer is 5, 6, and 7 and the second possible answer is -4, -3, and -2
Step-by-step explanation:
let the three numbers be (x-1), x, and (x+1)
the product of the smallest and largest number is 17 more than 3 times the middle number, or
(x-1)(x+1) = 3x+17, or
x^2-1 = 3+17, or
x^2-3x-18 = 0
(x-6)(x+3) = 0
So x = 6 or -3
Then just subtract one and add one to get the other integers. the three numbers are 5, 6, and 7 or -4, -3, and -2
Answer: 9.97
Step-by-step explanation:
Don’t know I’m just answering thus because it doesn’t let me ask a question unless I answer a random question. Sorry
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
