# Find the complex number which satisfies the given equation

• chwala
In summary: I think I get it now. In summary, the problem is a sign error in the simultaneous equations, which led to incorrect solutions initially. The correct solution is x=3 and y=-2.
chwala
Gold Member
Homework Statement
see attached
Relevant Equations
complex numbers
Find the problem here; ( i do not have the solutions...i seek alternative ways of doing the problems)

ok, i let ##z=x+iy## and ##z^*= x-iy##... i ended up with the simultaneous equation;
##2x+y=4##
##x+2y=-1##

##x=1## and ##y=2##

therefore our complex number is ##z=1+2i##

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

Find the problem here; ( i do not have the solutions...i seek alternative ways of doing the problems)

View attachment 297755ok, i let ##z=x+iy## and ##z^*= x-iy##... i ended up
How?
chwala said:
with the simultaneous equation;
##2x+y=4##
##x+2y=-1##

##x=1## and ##y=2##
##1+2\cdot 2 =5 \neq -1##
chwala said:
therefore our complex number is ##z=1+2i##

fresh_42 said:
How?

##1+2\cdot 2 =5 \neq -1##
let me check this...

Arrrgh
##x=3## and ##y=-2## ...sign error on my simultaneous equation...i guess its best to solve this questions over the weekend...i rush on this due to other work...

fresh_42 said:
How?
fresh from complex numbers we know that, if ##w=a+in## then ##w^* =a-in##

Last edited by a moderator:
I meant: How you ended up with these equations, not how conjugation is defined, i.e. show your steps.

fresh_42 said:
I meant: How you ended up with these equations, not how conjugation is defined, i.e. show your steps.
Ooh ok...noted Fresh...

## 1. What is a complex number?

A complex number is a number that consists of 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, defined as the square root of -1.

## 2. How do you solve an equation involving complex numbers?

To solve an equation involving complex numbers, you need to isolate the complex number on one side of the equation and the real number on the other side. Then, use algebraic operations to simplify the equation until you can find the value of the complex number.

## 3. What is the difference between a real number and a complex number?

A real number is a number that can be found on the number line, including both positive and negative numbers. A complex number, on the other hand, includes both a real part and an imaginary part and cannot be represented on a number line.

## 4. Can a complex number have a negative imaginary part?

Yes, a complex number can have a negative imaginary part. This means that the imaginary part is multiplied by -1, making it a negative value.

## 5. How do you graph a complex number on the complex plane?

To graph a complex number on the complex plane, you plot the real part on the x-axis and the imaginary part on the y-axis. This creates a point on the plane that represents the complex number.

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