How Do You Solve Complex Equations Involving Absolute Values?

In summary: Anyway, it looks like you have a typo there. It should be z_1=z+i, not z_1=z+1.In summary, the conversation is discussing how to solve for a complex number z, given two equations with one unknown. The equations involve the real and imaginary parts of z, and one equation includes a "part" notation which makes everything a^2 + b^2 and turns everything into "real." There is a suggestion to square both sides of the equations and then solve for the real and imaginary parts. Another suggestion is to split the complex number into real and imaginary parts from the beginning.
  • #1
transgalactic
1,395
0
http://img353.imageshack.us/img353/672/85253506or3.gif

in normal equation i equalize the "Real" part with the real part
and the "Im" part with the I am part on the other size of the equation
but here there is | | part

which makes every thing a^2 + b^2 and it turns everything to "real"

??
 
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  • #2
Why do you have 2 equations and 1 unknown?
 
  • #3
"z" is a complex number which i need to split into a real and imaginary parts
 
  • #4
Sorry, I'm not tracking you on this one. Why are there two equations shown?

WW = XX = YY

That overconstrains the solution for z. One equation should be enough to solve for z, it would seem?
 
  • #5
z is a complex number
its not a single variable
z=a+ib
i need to find Z
 
  • #6
Ah, I think I see now.

transgalactic said:
in normal equation i equalize the "Real" part with the real part
and the "Im" part with the I am part on the other size of the equation
but here there is | | part

which makes every thing a^2 + b^2 and it turns everything to "real"

Try squaring the whole side of each equation, and not the individual terms. You will still have real and imaginary parts to the squared equations.
 
  • #7
So like

z+i = z-1

z^2 + 2iz - 1 = etc. and gather terms on one side = 0

Then do the other equation, and you should be able to solve for RE{z} and Im{z}.
 
  • #8
It's probably easier to split it into to real and imaginary parts right off the bat. If z=a+bi, what is |z+i| in terms of a and b? How about the other two absolute values?
 
  • #9
You want the absolute value of [tex] z_1 [/tex] = z+1= a+(b+1)*i ?
 
  • #10
JANm said:
You want the absolute value of [tex] z_1 [/tex] = z+1= a+(b+1)*i ?

I'm going to guess you meant z+i=a+(b+1)*i, not z+1.
 

Related to How Do You Solve Complex Equations Involving Absolute Values?

1. What are complex numbers?

Complex numbers are numbers that have a real part and an imaginary part. They are written in the form a + bi, where a is the real part and bi is the imaginary part with i being the imaginary unit.

2. How do I add or subtract complex numbers?

To add or subtract complex numbers, you simply combine the real parts and the imaginary parts separately. For example, (2 + 3i) + (4 + 5i) = (2+4) + (3i+5i) = 6 + 8i. To subtract, you follow the same process but subtract the second complex number from the first.

3. How do I multiply complex numbers?

To multiply complex numbers, you use the FOIL method from algebra. First, you multiply the first terms, then the outer terms, then the inner terms, and finally the last terms. For example, (2 + 3i)(4 + 5i) = 8 + 10i + 12i + 15i^2 = 8 + 22i - 15 = -7 + 22i.

4. How do I divide complex numbers?

To divide complex numbers, you use the conjugate of the denominator. The conjugate of a complex number a + bi is a - bi. Multiply the numerator and denominator by the conjugate of the denominator, and then simplify. For example, (2 + 3i) / (4 + 5i) = (2 + 3i)(4 - 5i) / (4 + 5i)(4 - 5i) = (8 - 10i + 12i - 15i^2) / (16 - 25i^2) = (8 + 2i) / 41 = 8/41 + (2/41)i.

5. How do I graph complex numbers on the complex plane?

To graph complex numbers on the complex plane, you plot the real part on the x-axis and the imaginary part on the y-axis. For example, the complex number 2 + 3i would be graphed as a point on the complex plane at (2,3).

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