# Finding Complex Numbers: Solving Re(z) = 4Im(z)

• Jess Anon
In summary, to find three different complex numbers that satisfy the equation in the form a + bi, you can choose any three distinct values of 'b' and compute the corresponding values of 'a' using the equation a = 4b. This will give you three different complex numbers in the form a + bi that satisfy the given relationship. Alternatively, you can also use the variable 'n' instead of 'b' and have the complex numbers in the form 4n + ni for any real value n.
Jess Anon
Find three different complex numbers that satisfy the equation in the form a + bi.

I know that:
Re(z) = a + bi = a
Im(z) = a + bi = b
Re(z) = 4Im(z)
a = 4b
I'm stuck after this point.
How do you find what is a and what is b?

I don't understand the question.
For every ##x##, the complex number ##z=4x+ix## satisfies ##Re(z)=4Im(z)##
If you want three different ones, pick three distinct ##x##.

I need the find the complex number z that satisfy the equation, therefore I do not think that using any 3 x is the correct way.

Is ##Re(z)=4Im(z)## the only condition ?
If it is, then note that every ##x## satisifes the above condition with ##z=4x+ix##.

That's alright.
z = 4 + i which means that it is 4 times the imaginary part of z.
Hence z = 4n + ni for any real value n.

good for you :-)

Jess Anon said:
Find three different complex numbers that satisfy the equation in the form a + bi.

I know that:
Re(z) = a + bi = a
Im(z) = a + bi = b
Re(z) = 4Im(z)
a = 4b
I'm stuck after this point.
How do you find what is a and what is b?
In future posts, please follow the format of the homework template, with a complete description of the problem in part 1 (not in the thread title), any relevant formulas or equations in part 2, and your work in part 3. The use of the homework template is required for homework problems.

Jess Anon said:
Find three different complex numbers that satisfy the equation in the form a + bi.

I know that:
Re(z) = a + bi = a
Im(z) = a + bi = b
Re(z) = 4Im(z)
a = 4b
I'm stuck after this point.
How do you find what is a and what is b?

You were asked to find three different complex numbers satisfying the given relationship. So, what is preventing you from just using three different numerical values of 'b' (choose any three you like) and then computing the corresponding values of 'a'?

Jess Anon said:
That's alright.
z = 4 + i which means that it is 4 times the imaginary part of z.
Hence z = 4n + ni for any real value n.
Just curious — in your mind, how is this different from what @certainly suggested, other than replacing the variable ##x## with the variable ##n##?

## 1. What is the equation for finding complex numbers?

The equation for finding complex numbers is Re(z) = a + bi, where Re(z) represents the real part of the complex number and Im(z) represents the imaginary part.

## 2. How do you solve Re(z) = 4Im(z)?

To solve Re(z) = 4Im(z), you can use algebraic methods to isolate the real and imaginary parts of the complex number. This will result in a solution in the form of a + bi, where a and b represent the real and imaginary parts of the complex number respectively.

## 3. What is the significance of finding complex numbers?

Finding complex numbers is important in many scientific and mathematical fields, such as engineering, physics, and economics. They are used to represent quantities that have both real and imaginary components, and can be used to solve various equations and problems.

## 4. Can complex numbers have a real part of 0?

Yes, complex numbers can have a real part of 0. This means that the complex number is purely imaginary, and can be written in the form bi, where b is the imaginary component.

## 5. How are complex numbers represented on a graph?

Complex numbers can be represented on a graph using the complex plane, where the real part is plotted on the x-axis and the imaginary part is plotted on the y-axis. This allows for visualizing and understanding the relationships between complex numbers.

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