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

[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?

 

[certainly]

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 $x$.

 

[Jess Anon]

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.

 

[certainly]

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

 

[Jess Anon]

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

 

[certainly]

good for you :-)

 

[Mark44]

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.

 

[Ray Vickson]

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'?

 

[vela]

That's alright.
I figured it out already.
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 $n$?