MHB Help Me Solve $\text{Im}(z^3)$ in Rectangular Form

[Drain Brain]

I don't how to proceed further

Let $z=x+jy$ find in rectangular form:

1. $\text{Im}(z^3)$

this is where I can get to,

$\text{Im}(x^3+3x^2jy+3xj^2y^2+j^3y^3)=\text{Im}(x^3+3x^2jy-3xy^2-jy^3)$

please help me.

 

[Prove It]

I don't how to proceed further

Let $z=x+jy$ find in rectangular form:

1. $\text{Im}(z^3)$

this is where I can get to,

$\text{Im}(x^3+3x^2jy+3xj^2y^2+j^3y^3)=\text{Im}(x^3+3x^2jy-3xy^2-jy^3)$

please help me.

So what are the terms which have a "j" part?

 

[I like Serena]

I don't how to proceed further

Let $z=x+jy$ find in rectangular form:

1. $\text{Im}(z^3)$

this is where I can get to,

$\text{Im}(x^3+3x^2jy+3xj^2y^2+j^3y^3)=\text{Im}(x^3+3x^2jy-3xy^2-jy^3)$

please help me.

Hi Drain Brain! :)

You're already there:
$$\text{Im}(x^3+3x^2jy-3xy^2-jy^3) = \text{Im}((x^3-3xy^2)+(3x^2y-y^3)j)
= (3x^2y-y^3)$$

 

[Drain Brain]

they are $3x^2yj-j^3$ is this the answer?

 

[kaliprasad]

they are $3x^2yj-j^3$ is this the answer?

no .as I like serena mentioned it is
$3x^2y- y^3$ because imaginary part of $x+jy$ is $y $