maths help needed! badly!

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i have been set some questions and there are 2 questons which i cannot do, and its due 2moro!!!!!

Express z=j in polar form.
Hence find all the fourth roots of z(i.e.z^(1/4).
Illustrate z and its fourth roots clearly on an Argand diagram.
(10 marks)

(b) Find and simplify
(1+j)^2, (1+j)^3, (1+j)^4, (1+j)^5

Show that e^x(cosx+jsinx)=e^(1+j)x

By making an appropriate substitution in the power series for e^x, obtain the power series for e^x cosx and e^x sinx as far as the term in x^5 .
(You may quote the Maclaurin expansion for from KU tables.)

can some help me do this please???
 
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I'd presume it's in cartesian form?

so you have something like a-bj.

which you convert to polar form using r=sqrt(a²+b²) and theta = tan-1(b/a)
and then doing r(cos(theta) - jSin(theta)).
 
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Post exactly what you've done, and where you're stuck.

No-one (I hope) is going to do your homework for you unless you put in some effort yourself.
 
DaveF said:
Post exactly what you've done, and where you're stuck.

No-one (I hope) is going to do your homework for you unless you put in some effort yourself.
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i havent done any work on polar series thats the problem. i missed the uni lecture and cant find the notes for it
 
the_one_deep86 said:
i havent done any work on polar series thats the problem. i missed the uni lecture and cant find the notes for it
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Have you covered e^(ix) = cos(x) + i sin(x)?

Polar form is just rewriting a+ib in the form r e^it. (If you draw (a+ib) as a position in the complex plane, then r is the distance from the origin, t is the angle from the horizontal axis).

There's an introduction at http://en.wikipedia.org/wiki/Complex_number - haven't looked closely, but I'm sure it's pretty accurate.

With all respect to Phnom_Penh, at least part of what he's written is wrong and the other bit is decidedly non-standard, so if I were you, I'd have a look at the wiki page.
 
DaveF said:
With all respect to Phnom_Penh, at least part of what he's written is wrong
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It is? Where lol.

The only part I didn't say was where you add a multiple of 90 to theta, but from the wiki,

d061453b9e97cfb3e1ce8b196a14247a.png

5ad5784bd692bfaad41bae72ab8bafdf.png

5d6cd86d52a1488522279a84c0a6f640.png


Edit : he didn't have the equations in before :grumbles:. :p
 
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the_one_deep86 said:
(b) Find and simplify
(1+j)^2, (1+j)^3, (1+j)^4, (1+j)^5
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Essentially you're just multplying them together (I presume lol)

so it would be..

(1+j)(1+j)
= 1 + 1j + 1j + -1 (as j² = -1)
= 0 + 2j.

and then the next one (^3) would be...

(1+j)(1+j)(1+j) or (0+2j)(1+j). (they seem to give different results :\).
 
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Phnom_Penh said:
It is? Where lol.
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Your formula for r is wrong (you've multiplied a^2 by b^2 instead of adding). (Oh, I see you've now fixed it. LOL).

You've also used a - ib and cos t - i sin t, whereas the standard is a + ib and cos t + i sin t.

I don't doubt you actually know what you're doing, and the mistakes are just formatting problems. But that's all the more reason to use the wiki site, as it can use proper mathematical notation and provide diagrams.
 
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the_one_deep86 said:
i havent done any work on polar series thats the problem. i missed the uni lecture and cant find the notes for it
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Why did you wait until the night before to ask? You should have gone to ask the lecturer...
 
DaveF said:
Your formula for r is wrong (you've multiplied a^2 by b^2 instead of adding). (Oh, I see you've now fixed it. LOL).

You've also used a - ib and cos t - i sin t, whereas the standard is a + ib and cos t + i sin t.

I don't doubt you actually know what you're doing, and the mistakes are just formatting problems. But that's all the more reason to use the wiki site, as it can use proper mathematical notation and provide diagrams.
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Teehee :p. Noticed that one. If b is negative, then it's going to be a-jb, and I *think* it would be cos(t) - j sin (t), you might be able to answer this one though, if the angle you have is negative (-25), and it's in say the second quadrant, so you add 90, should you have -115 (I presume you don't want to have 65)?
 
Phnom_Penh said:
Teehee :p. Noticed that one. If b is negative, then it's going to be a-jb, and I *think* it would be cos(t) - j sin (t), you might be able to answer this one though, if the angle you have is negative (-25), and it's in say the second quadrant, so you add 90, should you have -115 (I presume you don't want to have 65)?
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I don't know where you're getting "b is negative" (in fact, I see no mention of b in the original post), so it's a bit hard to comment.

The "standard" notation for a complex number is a+ib, which can also be written as r e^it = r (cos(t) + i sin(t)). Here a, b can be any real number, either positive or negative; the whole point about the representation is that it's consistent.

If you're doing it right, you shouldn't ever have to worry about quadrants, etc, unless you're doing something odd with multivalued functions. I don't know why you're worrying about adding 90 either. To be honest, I don't really know what you're trying to do with your calculations - are you trying to answer the OP's question?
 
Well, I'm still guessing at what you're trying to do, but if you're talking about the change in argument when you multiply by i, then you always add.

E.g. (1-i) corresponds to argument -45. Multiply by i and you get 1+i which is argument 45.
 
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