The discussion focuses on finding the imaginary part of the expression $\text{Im}(z^3)$ where $z = x + jy$. The key conclusion is that the imaginary part simplifies to $(3x^2y - y^3)$. This result is derived from the expansion of $z^3$ and identifying the terms containing the imaginary unit $j$. The final answer confirms that the imaginary component is indeed $3x^2y - y^3$.
PREREQUISITESStudents of mathematics, particularly those studying complex analysis, as well as educators and anyone interested in the properties of complex numbers and their applications.
Drain Brain said: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.
Drain Brain said: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.
Drain Brain said:they are $3x^2yj-j^3$ is this the answer?