The square root of (1-8i) is, wait for it, another complex number!astrololo said:Homework Statement
z^6+(2i-1)z^3-1-i=0
Homework Equations
The Attempt at a Solution
I know that I must put k=z^3 and solve the quadratic. But I'm not able to simplify the quadratic. I get the square root of (-8i+1)
What am I supposed to do ?
Check that result from quadratic formula again.astrololo said:Homework Statement
z^6+(2i-1)z^3-1-i=0
Homework Equations
The Attempt at a Solution
I know that I must put k=z^3 and solve the quadratic. But I'm not able to simplify the quadratic. I get the square root of (-8i+1)
What am I supposed to do ?
Right. The imaginary part doesn't include the imaginary unit, i , by the usual convention.Ian Taylor said:ogg, I think you meant to write:
Re##(z)=a^2-b^2## and Im##(z)=2ab##
Thanks SammyS. He had also written ##z^2## rather than ##z##. which contradicts his original definition.SammyS said:Right. The imaginary part doesn't include the imaginary unit, i , by the usual convention.
Hello, Ian Taylor. Welcome to PF !
If you notice, this thread is 1/2 year old.
A polynomial with complex coefficients is an algebraic expression that contains a variable raised to different powers, with coefficients that are complex numbers. Complex numbers are numbers that consist of a real part and an imaginary part, and are written in the form a + bi, where a and b are real numbers and i is the imaginary unit.
To solve a polynomial with complex coefficients, you can use the same methods used for solving polynomials with real coefficients. This includes factoring, using the quadratic formula, and completing the square. However, since complex numbers have both a real and imaginary part, the solutions will also have both a real and imaginary part.
The steps for solving a polynomial with complex coefficients are:
1. Simplify the polynomial by combining like terms
2. Factor the polynomial, if possible
3. Set each factor equal to 0 and solve for the variable
4. Use the quadratic formula or completing the square, if necessary
5. Write the solutions in the form a + bi
Yes, you can use the same methods for solving polynomials with complex coefficients as you would for polynomials with real coefficients. However, the solutions for polynomials with complex coefficients will involve both real and imaginary numbers, while the solutions for real coefficients will only involve real numbers.
It is important to consider complex coefficients when solving polynomials because complex numbers are used to represent many real-world phenomena, such as electrical currents and AC circuits. Solving polynomials with complex coefficients allows us to accurately model and understand these phenomena, and to find the solutions to equations involving complex numbers.