Question

can anyone give me some formulas/solution to review on?

topic is :
complex numbers
series and sequences

please?

Answer 1

What's your depth in these topics?

Answer 2

what do you mean?
can you help me ? :( i have to review for our exam but sadly i have no notes and i forgot to borrow one...

Answer 3

For complex numbers,
-----------------------------------
\[i^2=-1, \sqrt{-1}=i\]
-----------------------------------
1) Equality of complex numbers
a + bi = c + di if and only if a = c and b = d
So,
a-c+bi-di=0
(a-c)+i(b-d)=0

2) Addition of complex numbers
(a + bi) + (c + di) = (a + c) + (b + d)i
3) Subtraction of complex numbers
(a + bi) - (c + di) = (a - c) + (b - d)i
4) Multiplication of complex numbers
(a + bi)(c + di) = (ac - bd) + (ad + bc)i
5) Division of complex numbers, multiply with the conjugate of denominator
\[\frac{a+bi}{c+di}=\frac{a+bi}{c+di} \times \frac{c-di}{c-di}=\frac{ac-adi+bci-bdi^2}{c^2-d^2i^2} \\ \\ \frac{ac-adi+bci+bd}{c^2+d^2} \\ \\ \frac{(ac+bd)+i(bc-ad)}{c^2+d^2}\]

Answer 4

If you have z=a+bi and you want to find the modulus and argument,
Modulus |z|, formula is
\[|z|=\sqrt{a^2+b^2}\]
Argument formula, arg(z) is
\[\arg(z)=\tan^{-1}\frac{b}{a}\] You then sketch an argand diagram based on the angle you get from arg(z),

Answer 5

@syhna Nevermind :) I'll just give out these basic/ fundamentals of complex numbers

Answer 6

thanks

Answer 7

Then we have converting between polar and cartesian coordinates,
If we sketch a graph like this,

From SOH CAH TOA,
\[\cos(\theta)=\frac{x}{r} \\ \\ x=rcos(\theta) \\ \\ \sin(\theta)=\frac{y}{r} \\ \\ y=rsin(\theta)\]