Question

. In this question, i ? C is the imaginary unit, that is, the complex number...

. In this question, i ? C is the imaginary unit, that is, the complex number satisfying i^2 = ?1. (a) Verify that 2 ? 3i is a root of the polynomial f(z) = z^4 ? 7z^3 + 27z^2 ? 47z + 26 Find all the other roots of this polynomial. (b) State Euler’s formula for e^i? where ? is a real number. (c) Use Euler’s formula to prove the identity cos(2?) = cos^2 ? ? sin^2 ? (d) Find all solutions to z^3 = 1 in both polar form (z = re^i?, where r > 0 and 0 ? ? < 2? are real numbers) and rectangular form (z = a + ib, where a and b are real numbers).

Math   Algebra   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Please Use C++ I tried to calculate complex number by using *= and operator /= but...
Please Use C++ I tried to calculate complex number by using *= and operator /= but I got an incorrect result compared with the result of complex number calculator For example, When I calculate ( (c5 *= c4) *= c4) by using my operator function, the result was 1.08288e+06+1.11262e+07i on output, However, when using a complex calculator, the result was = −253987.448 − 355181.112i, so I got the wrong answer There is my code below. It compiles well, but my...
When plotted in the complex plane for , the function f () = cos() + j0.1...
When plotted in the complex plane for , the function f () = cos() + j0.1 sin(2) results in a so-called Lissajous figure that resembles a two-bladed propeller. a. In MATLAB, create two row vectors fr and fi corresponding to the real and imaginary portions of f (), respectively, over a suitable number N samples of . Plot the real portion against the imaginary portion and verify the figure resembles a propeller. b. Let complex constant w = x +...
So if we can find a number r satisfying r2=b2−4ac, then we can solve for z...
So if we can find a number r satisfying r2=b2−4ac, then we can solve for z in terms of a,b,c and r as z=−b2a±r2a. Hopefully you can recognize the usual quadratic formula here. If b2−4ac is a positive real number, we usually just replace r with b2−4ac−−−−−−−√. However if b2−4ac is a negative real number, or in fact a general complex number---which will happen if a,b and c are complex numbers---then there is no canonical b2−4ac−−−−−−−√, but we could still...
I need to write a c++ segment to calculate the phase angle of a complex number...
I need to write a c++ segment to calculate the phase angle of a complex number on the interval [0, 2pi). The segment needs to return -1 when the phase is undefined. I am having trouble figuring out how to adjust a number outside of the interval and get it into the interval (i.e. add 2pi, add pi, etc). This is what I have so far:    if (real == 0 && imag==0)    {        return -1;   ...
Fix a positive real number c, and let S = (−c, c) ⊆ R. Consider the...
Fix a positive real number c, and let S = (−c, c) ⊆ R. Consider the formula x ∗ y :=(x + y)/(1 + xy/c^2). (a)Show that this formula gives a well-defined binary operation on S (I think it is equivalent to say that show the domain of x*y is in (-c,c), but i dont know how to prove that) (b)this operation makes (S, ∗) into an abelian group. (I have already solved this, you can just ignore) (c)Explain why...
Basic probability for Discrete math problem: (I am mostly interested in part c,d,and e if you...
Basic probability for Discrete math problem: (I am mostly interested in part c,d,and e if you can't do them all. will rate asap) Imagine a fictional scenario where a new area code 229 has just been assigned to Los Angeles. To request a phone number with this new area code, a computer program randomly generates a 7-digit number s1s2s3 − s4s5s6s7. That is for i = 1, 2, ... , 7, a random number generator picks a number from 0...
The decimal values of the Roman numerals are: M D C L X V I 1000...
The decimal values of the Roman numerals are: M D C L X V I 1000 500 100 50 10 5 1 Remember, a larger numeral preceding a smaller numeral means addition, so LX is 60. A smaller numeral preceding a larger numeral means subtraction, so XL is 40. Assignment: Begin by creating a new project in the IDE of your choice. Your project should contain the following: Write a class romanType. An object of romanType should have the following...
1. Suppose we have the following relation defined on Z. We say that a ∼ b...
1. Suppose we have the following relation defined on Z. We say that a ∼ b iff 2 divides a + b. (a) Prove that the relation ∼ defines an equivalence relation on Z. (b) Describe the equivalence classes under ∼ . 2. Suppose we have the following relation defined on Z. We say that a ' b iff 3 divides a + b. It is simple to show that that the relation ' is symmetric, so we will leave...
I have solved the problem up to number 6. all my answers from 7 keeps coming...
I have solved the problem up to number 6. all my answers from 7 keeps coming up incorrect. That is where i need the help. Thank you Note: This problem is for the 2018 tax year. Daniel B. Butler and Freida C. Butler, husband and wife, file a joint return. The Butlers live at 625 Oak Street in Corbin, KY 40701. Dan's Social Security number is 111-11-1112, and Freida's is 123-45-6789. Dan was born on January 15, 1967, and Freida...
Beth R. Jordan lives at 2322 Skyview Road, Mesa, AZ 85201. She is a tax accountant...
Beth R. Jordan lives at 2322 Skyview Road, Mesa, AZ 85201. She is a tax accountant with Mesa Manufacturing Company, 1203 Western Avenue, Mesa, AZ 85201 (employer identification number 11-1111111). She also writes computer software programs for tax practitioners and has a part-time tax practice. Beth is single and has no dependents. Beth was born on July 4, 1972, and her Social Security number is 123-45-6789. She wants to contribute $3 to the Presidential Election Campaign Fund. The following information...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT