# Find two possible values of ##z## in the complex number problem

• chwala
In summary, the conversation is about solving a quadratic equation with complex numbers. The specific equation is x^2+y^2-5x=0 and the solution is z=4-2i and z=1-2i. The person also mentions seeking a different approach but it is not clear what that approach might be. The other person suggests asking for a different approach and notes that the simultaneous approach used is the most obvious and simplest.
chwala
Gold Member
Homework Statement
see attached.
Relevant Equations
complex numbers
ok here i have,
##x^2+y^2-5x=0##
##-y= 2##
I end up with the quadratic equation, ##x^2-5x+4=0##

Finally giving us, ##z=4-2i## and ##z=1-2i##

Looks right.

chwala
chwala said:
Homework Statement:: see attached.
Relevant Equations:: complex numbers

Finally giving us s, ##z=4-2i## and ##z=1-2i##
Which is easy enough to check for yourself.

chwala
Thanks Mark...I am seeking for a different way of solving this apart from simultaneous approach that I used...that's why I posted the question...yes, I can check that mate.

chwala said:
Thanks Mark...I am seeking for a different way of solving this apart from simultaneous approach that I used...that's why I posted the question...yes, I can check that mate.
Then you should ask for a different approach, which you haven't gotten from us yet. This wasn't clear in your original post.

chwala
chwala said:
Thanks Mark...I am seeking for a different way of solving this apart from simultaneous approach that I used...that's why I posted the question...yes, I can check that mate.
What you did was the most obvious and simplest approach. If there is another way, I can't think what it might be.

Noted Mark...thanks for your time on this...

## 1. What is a complex number?

A complex number is a number that contains both a real part and an imaginary part. It is written in the form a + bi, where a and b are real numbers and i is the imaginary unit (i.e. √-1).

## 2. How do you find the real and imaginary parts of a complex number?

To find the real part of a complex number, simply take the number without the imaginary unit. To find the imaginary part, take the coefficient of the imaginary unit (i.e. the number in front of the i).

## 3. What is the standard form of a complex number?

The standard form of a complex number is a + bi, where a and b are real numbers and i is the imaginary unit. This form is used to easily identify the real and imaginary parts of a complex number.

## 4. How do you solve for z in a complex number problem?

To solve for z in a complex number problem, you can use the quadratic formula or factor the equation. Once you have found the solutions, you can plug them into the standard form a + bi to get the complex number.

## 5. How many possible values of z are there in a complex number problem?

In a complex number problem, there are typically two possible values of z. This is because the quadratic formula produces two solutions, one for the positive square root and one for the negative square root.

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