Help solving a complex equation

In summary, Daniel is trying to solve an equation that has three solutions that all equal zero. He has been trying to find the last solution, which is (x=-i). However, when he tries to solve the equation, he keeps getting different answers. All of the answers are non-zero.
  • #1
Yura
39
0
im not sure i can fully remember the rules for complex numbers but i have to solve an equation that has 3 solutions to equal zero. so far i have (x=2), (x=i) and i think there was a + rule for a solution with complex numbers that there would always be a conjugate solution of it. so i figured that the last solution would be (x=-i) but when i try and solve it i keep getting different answers and they are all non zero.

i think i may be doing something wrong with the powers of the (-i) or it might be that i thought wrong and (x=-i) is not a solution.

could someone please confirm ths for me?

here is the equation:
x^3 - (2-i)*x^2 + (2-2*i)*x - 4 = 0

im trying to solve for:
(-i)^3 - (2-i)*(-i)^2 + (2-2*i)*(-i) - 4 = 0

thanks in advance ^^
 
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  • #2
No,it doesn't have real coefficients.

Dividing the polynomial

[tex]x^{3}-(2-i)x^{2}+(2-2i)x-4 [/tex] by [tex] (x-2) [/tex]

u get the polynomial [tex] x^{2}+ix+2 [/tex] which has the solutions [tex] x_{1}=i [/tex] and [tex]x_{2}=-2i [/tex] .


Daniel.
 
  • #3
You really shouldn't try to merely remember rules, you should understand them in the first place!
You cannot use the "conjugate rule" here (when does that one apply?)

To give you a hint:
Use polynomial division to determine the last root.

EDIT:
Daniel is a real polynomial divisionist, a rather complex person, actually.
He doesn't need reminders in order to find remainders..
 
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  • #4
ah ok thankyou ( i had actually tried polynomial long division first but half way through i remembered my one of my teachers saying something about a conjugate rule for it so i stopped and tried that first) now that i try the division i find it works out fine, so i'll have to look up that rule and see if it works or not

thanks again
 
Last edited:

Related to Help solving a complex equation

1. How do I know which method to use to solve a complex equation?

The method you use to solve a complex equation depends on the type of equation and the information given. Some common methods include factoring, substitution, elimination, and graphing. It is important to carefully read the equation and gather all given information before deciding on a method.

2. What is the order of operations when solving a complex equation?

The order of operations, also known as PEMDAS (parentheses, exponents, multiplication/division, addition/subtraction), should be followed when solving a complex equation. This means that any operations within parentheses should be completed first, followed by exponents, then multiplication and division from left to right, and finally addition and subtraction from left to right.

3. What do I do if I get stuck while solving a complex equation?

If you get stuck while solving a complex equation, it is important to double check your work and go back to the beginning to see if you missed any steps. You can also try using a different method or asking for help from a teacher or tutor. It is important to stay patient and persistent when solving complex equations.

4. Can I use a calculator to solve a complex equation?

Yes, a calculator can be a helpful tool when solving a complex equation. However, it is important to make sure the calculator is set to the correct mode (standard, scientific, etc.) and that you understand how to input the equation and interpret the results. It is also important to show your work and not solely rely on the calculator.

5. How can I check if my solution to a complex equation is correct?

To check if your solution to a complex equation is correct, you can substitute the value you found for the variable back into the original equation. If the equation is true, then your solution is correct. You can also use a graphing calculator or online graphing tool to check for any intersections between the equation and the line or curve it represents.

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