Tutorial Week 8 - curve sketching ch7

 

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 :-)

Mobius calculuc question

 

Complex numbers - examples

Thanks to students for these contributions :-)

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$\infty\ \ \ \ \ $ How to Study Mathematics 1A $\ \ \ \ \ \infty$

 

Consultation Times and Rooms

CONSULTATIONS Reminder:  

• WEDNESDAY 2-3PM - B116 - Blockhouse  (and Virtual Classroom)
• FRIDAY 3:30-4:30PM - B219 -Blockhouse (and  Virtual Classroom)

It is best practice to make an attempt at solving a problem before asking for instructions in consultations or question forum.

Correct as at 8 June 2023. Consult the Teams page for any updates.

class test question - Cross Product in $\mathbb{R}^3$ and area of parallelogram.