4U Maths Question Thread

[RuiAce]

Hello!
I would like to know if using cis is possible for complex numbers.

Yeah for HSC MX2 this is fine

[frog1944]

Hi Rui,

I read somewhere that apparently it causes issues later on at university using the cis notation? Is this correct?

Thanks

[Dragomistress]

May you also do this:
Solve the equation z^3=1 when z=x+yi using the De Moivre's Theorem to find the roots of complex numbers.

[frog1944]

[frog1944]

I've tried to post my solution, however, the formatting for LaTex doesn't seem to be working for me (any help what I did wrong)?

[Dragomistress]

Ha ha, thanks for trying though. Can you try just take a photo of it instead as I sort of need it very soon.

[frog1944]

Sorry, it should be working now

[RuiAce]

Hi Rui,

I read somewhere that apparently it causes issues later on at university using the cis notation? Is this correct?

Thanks

The "cis" notation is an extremely redundant notation and nobody uses it in the real world. Writing it as the complex exponential takes less time so you should always go about that instead. The reason why "cis" gets taught in high school is because to actually prove Euler's formula you need Taylor series, which will certainly not go into high school math.

Honestly a bit of a lame excuse, but there's not much we can do about it.

[Jeeffffffffffffff]

Hey guys, would anybody be keen to help me with some subset graphing?
the question says to illustrate the following subsets of C on the z-plane and one of them is:
Arg[z-(1-iroot3)]=2pi/3
I've been shown a couple ways of how to do these types of questions but I was just after an easy method that will work everytime

[RuiAce]

Hey guys, would anybody be keen to help me with some subset graphing?
the question says to illustrate the following subsets of C on the z-plane and one of them is:
Arg[z-(1-iroot3)]=2pi/3
I've been shown a couple ways of how to do these types of questions but I was just after an easy method that will work everytime

So you'd have the ray drawn from \( 1-\sqrt3 i \) making an angle of \( \frac{2\pi}3 \) with the positive real axis.

[Jeeffffffffffffff]

So you'd have the ray drawn from \( 1-\sqrt3 i \) making an angle of \( \frac{2\pi}3 \) with the positive real axis.

Awesome, cheers Rui.

[itssona]

for any complex numbers z1,z2, show that |z1+z2|^2 + |z1-z2|^2 = 2(|z1|^2 + |z2|^2)
thank you

[RuiAce]

for any complex numbers z1,z2, show that |z1+z2|^2 + |z1-z2|^2 = 2(|z1|^2 + |z2|^2)
thank you

[itssona]

thank u Rui

[Jeeffffffffffffff]

2i(y-1)>0

Can you divide by 2i and keep the inequality the same?

To give y>1

Or is there something I'm missng?