By using Euler's notation, we will see that:
z^7 = 78,125*e^(-i*4.48)
<h3>
How to get z^7?</h3>
We know that:
z = 4 - 3i
Remember that for a complex number:
w = a + bi
In Euler's notation, we can write this as:
w = √(a^2 + b^2)*e^(i*Atan(b/a))
Then, for z, we will get:
z = √(4^2 + (-3)^2)*e^(i*Atan(-3/4))
z = 5*e^(-i*0.64)
Now, if we apply an exponent of 7 to this number, we will get:
z^7 = ( 5*e^(-i*0.64))^7
z^7 = 5^7*e^(-i*7*0.64) = 78,125*e^(-i*4.48)
If you want to learn more about complex numbers, you can read:
brainly.com/question/10662770
Answer:
b=-19
Step-by-step explanation:
We know that one of the solutions is x=-4/5
That is a solution to x. So if we plug in (-4/5) into the x in the equation, then it should equal 0.
5(-4/5)^2+b(4/5)+12=0
Now, just solve for b.
5(16/25)+b(4/5)+12=0
(16/5)+(4/5)b+12=0
(76/5)+(4/5)b=0
(4/5)b=-(76/5)
b=-19
Answer:
3/8
Step-by-step explanation:
Step 1: Find common denominators
1/2 = 4/8
2/4 = 4/8
Step 2: Evaluate
4/8 + 4/8 - 5/8
8/8 - 5/8
3/8
Alternatively, you can just plug this into a calc to evaluate and get your answer.
Sets II, III, and IV are all representations of functions.
The first thing is to define each one:
Polynomial: expression made with constants, variables and exponents, which are combined using addition, subtraction and multiplication. Exponents can only be natural numbers and the polynomial cannot have an infinite number of terms.
Example:
This is a: 
Degree: It is the exponent with the highest degree. If a monomial of those that are forming the polynomial has two unknowns, each with its exponent, these add up since we would be doing a multiplication of monomials.
Example: 
The degree of this polynomial is 3 because it is the largest exponent.
Linear term coefficient: is the number that multiplies the variable with the highest exponent
Example: 
In this case it is 5 because
is the variable with the highest exponent
Constant term coefficient: is one that is found in a polynomial alone, that is, without multiplying the x or another unknown.
Example: 
In this case it is 20 because it is the one found without multiplying any linear term (x)
Attached image with example of this.