HI everyone.
Raza Here.. i m new to Math Help Forum..
actually im a student of B.CS and facing so many problems nowadays in calculus..
so i m here to discuss my problems to u all... so please kindly help me out..
i'll be very thankful to u all..

Problem:1

Q#1(a): Convert the following complex numbers into polar form and sketch.

(i) 2-3i/5-4i (ii) 1/2 - root(3)i/2

(b): Find five 5th roots of ‘-1’.

Q#2(a): Find limit

(i) lim(x->0) Sin6x/Sin8x (ii) lim(x->0) x^2/1-Cosx

(b): Show That y = x^3 + 3x + 1 satisfies y'''+xy''-2y'=0

Q#3(a): Expand f(x) = ln(x+2) in the power of (x – 3).

(sorry! i didnt find a symbol for under-root thats y i only write root (in question 1) so please realize this as a under root of 3i)

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Raza Elahi

2. for 1 and 2, you need to combine the real and imaginary parts into like terms (1 real part 1 imaginary part) and think of these as cartesian coordinates. Do you know how to go from cartesian to polar?
$\displaystyle r=sqrt{x^2+y^2}$
$\displaystyle \theta = arctan(y/x)$

The complex number then is $\displaystyle re^{i\theta}$

fifth roots are the zeroes of $\displaystyle z^5+1$
Use polar coordinates for complex.
$\displaystyle -e^{\frac{i2\pi k}{5}}$ for k=0,1,2,3,4

Use L'hospital's rule once on the first and twice on the second, you should get 3/4 and 2 respectively

plug and chug dude, y"' is the third derivative start doing it unless you dont know what a derivative is, it is a polynomial so if you have any clue of calculus you should be able to take those derivatives, if not, let us know and we can explain that. Although thinking about it, if you cant do this there is no way you will be able to use l'hospital's rule, so lets hope for the best.

I don't understand your last question? You talking about power series expansions? Taylor series.