Complex numbers with an unknown, fraction equation not getting it right

In summary, the conversation was about attempting a solution for a given problem, where the manual stated that the answer is -1 + i. However, the solution provided was not simplified and the person providing the solution was reminded to multiply the top and bottom by the conjugate. After some corrections, the correct solution was found and the person was grateful for the reminder to treat i and z like x and y and to turn i^2 into -1.
  • #1
Femme_physics
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Attempt solution attached
Manual says the answers is -1 + i
 

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  • #2
The solution you posted,
[tex]z = \frac{2}{1 + i}[/tex]
is not simplified. You know that you can multiply top and bottom by the conjugate, right? Even so, you still won't get the right answer.

EDIT: I think I found it. From the 2nd to 3rd line, on the RHS you have
[tex](2iz + 1)(1 - i) = 2iz - 2iz + 1 -i [/tex]
, which is wrong. It should be
[tex](2iz + 1)(1 - i) = 2iz - 2i^2 z + 1 - i[/tex]
.
 
Last edited:
  • #3
Thanks for the great catch! :) I wasn't sure I even know how to solve these. Glad to see I didn't do anything horribly wrong. Apparently it's all about treating i and z like x and y, and if i ever gets to the power of 2, just turn into -1. Easy peasy :)

Appreciate you taking the time to spot my carelessness!
 

What are complex numbers?

Complex numbers are numbers that have both a real and imaginary component. They are written in the form of a + bi, where a is the real part and bi is the imaginary part.

What is an unknown in a fraction equation?

An unknown in a fraction equation is a variable that represents a number that is not known. It is usually denoted by a letter, such as x or y, and is solved for using algebraic methods.

How do you solve an equation with complex numbers?

To solve an equation with complex numbers, you must first isolate the complex number by moving all other terms to the other side of the equation. Then, use mathematical operations to solve for the unknown variable.

Why am I not getting the right answer when solving an equation with complex numbers?

There could be several reasons for this. Some common mistakes include not following the correct order of operations, not properly distributing a negative sign, or making a calculation error. It is important to double check your work and make sure all steps are correct.

How can I improve my understanding of complex numbers and fraction equations?

Practice is key when it comes to understanding complex numbers and fraction equations. Try solving a variety of equations and problems to become more comfortable with the concepts. You can also seek help from a tutor or online resources for additional support.

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