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#1 2006-05-01 01:27:48

xena
Guest

problem question

i really really need help with this please.....

Given   Z1=2+i4
           
           Z2=6-i3

           Z3=3-i5


If possible can someone help me with this,

its asking to determine the following

a] Z1+Z2

b] Z1+Z2+Z3

c] Z1 -Z2

d] Z1-Z2-Z3

e] Z1 . Z2

f] Z1/Z2

g] Z3-Z2-Z1

h] it says find,Z1 +Z2 + Z3 and Z3 -Z2 - Z1 on an argard diagram 


thank you...

#2 2006-05-01 02:06:25

renjer
Member
Registered: 2006-04-29
Posts: 51

Re: problem question

Complex numbers addition and subtraction, think about this as normal algebra. Eg: a+a=2a, a+b=a+b.
For your example: Z1+Z2=2+4i+6-3i=(2+6)+(4-3)i=8+i

For multiplication, just do it as normal algebra, except, remember that i^2=-1. So anywhere you have an i^2, replace with -1, and you're on your way.

Division would be the hardest of all. Have you learnt about conjugates? Take the conjugate of Z2, i.e., 6+3i and set up your equation like in the picture. Now do the same thing as with multiplication, treat it as if it is algebra, only remember to replace i^2=-1.

For Argand diagrams, first find the product of the equation eg, for Z1+Z2+Z3, you would have found the answer in (b). Plot the x and y coordinates, put the real part on the x coordinate and imaginary part on the y coordinate. Eg, for 3+4i (it's not the answer), I would plot the point (3,4). Then connect a line from the origin (0,0) to the point you've plotted, put an arrow in its direction, and you have your answer.

View Image: b.jpg

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#3 2006-05-01 02:14:56

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: problem question

Here are a few simple rules for complex algebra:




Edit:

But understanding why these rules are so is infinitely more benefical then memorizing them.

Last edited by Ricky (2006-05-01 02:16:18)


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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