Challenge:Complex reducible to quadratic equation: Solve $$z^4+2\left(a^2-b^2\right)z^2+\left(a^2+b^2\right)^2=0$$ where $a,b\in\mathbb{R}$

Solve $$z^4+2\left(a^2-b^2\right)z^2+\left(a^2+b^2\right)^2=0$$ where $a,b$ are real numbers.

Hint 1 : Put $w=z^2$ and find $w$ first.  Then for each $w$, solve $z^2=w$.

Hint 2: see other posts on this label.

Answer: $z=\pm (a+ib), \pm (a-ib)$

Complex reducible to quadratics equation: Solve $$z^4+16z^2+100=0$$ .

Question: Solve $$z^4+16z^2+100=0$$ .

Show the answers are $$z=\pm(1+3i), \pm(1-3i)\ \ .$$

Complex reducible to quadratic equation: Solve $$z^4+12z^2+169=0$$

 

Try solving this one now

$$z^4+16z^2+100=0$$ and show the solutions are ....https://dipa2023t2.blogspot.com/2023/06/complex-reducible-to-quadratics.html

Mobius antiderivative question

Let me know if this makes sense :-)