ahrd question?? (1 Viewer)

[bos1234]

Show that i^n, when n is integral. has one of four values plus or minus 1 and plus or - i



solve for w1 and w2

2w1 + 3iw2 = 0
(1-i)w1 + 2w2 = i-7

 

[SoulSearcher]

I would assume that when n is an integral number.

 

[bos1234]

thanks for the working out. Appreciate it. The second question w1 w1..

it has a asterix next to it meaning that its a hard question.. so well done!!!!!

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here is another :S
how do i do this one?

http://img83.imageshack.us/img83/4843/ash6.png

 

[bos1234]

well done.. can any1 beat 11 lines???

HOW DO I DO THIS QUESTION??

Express the roots of the following equations in the form a+ib

i)x^2-3x+10i=0

 

[Affinity]

for:
2w1 + 3iw2 = 0
(1-i)w1 + 2w2 = i-7
not really, lottox's way is quite short already.. he just made it long to explain it

x^2-3x+10i=0

the hard part is to take the squareroot of 9-40i which after some thoughts gives you sqrt(9-40i) = (5-4i) or (-5+4i)

(well you want to solve a^2 - b^2 = 9 and 2ab=40, easy)

 

[Wackedupwacko]

remember my friend your quadratic formula is your friend. and also being able to sqrt complex numbers which like affinity says is just solving the simulatenous eqns of a^2 - b^2 = Re(z)
and 2ab = Im(z)

after that there shouldnt be any quadratic you cant do.

 

[Affinity]

personally I find it harder to spot that (1-2i)+(-4+2i) = -3 and their product = 10i