Understanding Complex Numbers for Solving Problems

In summary, the conversation involved solving for the variable z using the given equation and tips provided by the expert. The final solution was z=1+i, with the use of the conjugate and multiplying on both the top and bottom. The individual expressing gratitude and appreciation for the expert's help.
  • #1
meee
87
0
need a lil help here

thnx
 
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  • #2
Set g(z)=z, that is, write 2 + zi = z and then solve for z.
 
  • #3
ok.. thanks, any tips in solving for z?

i got.. z = 2 + zi
z/z = 2/z + i
1 = 2/z + i
2/z = 1 - i
z= 2/(1-i)

dont think I am going the right way
 
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  • #4
[tex]2 + iz = z[/tex]
[tex]2 = z -iz = z(1-i)[/tex]

and so, like you have

[tex] z= \frac{2}{1-i}[/tex]

now multiply by the conjugate of the denominator on top and bottom
 
  • #5
wel... we can divide 2 by (1 - i) to get z...OHHHhhhhhhhhhhhhhhhhhhhh ahhhhhhhhhh.!1 forgot that!1 multiple by conjugate... how silly of me

thankyou so much! !1

yaaay...

bottom: (1-i) * (1+i) = 2
top: 2*(1+i) = 2+2i

= (2+2i)/2
= 1+i

Yayaya Thnnx So mUcH!
 
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  • #6
[tex] z= \frac{2}{1-i} =\left( \frac{2}{1-i}\right) \left( \frac{1+i}{1+i} \right) = \frac{2(1+i)}{(1-i)(1+i)} = \frac{2(1+i)}{1^2-i^2} = \frac{2(1+i)}{1-(-1)} = 1+i[/tex]
 
  • #7
nice diagram!

tankyou somuch
 

FAQ: Understanding Complex Numbers for Solving Problems

What are complex numbers?

Complex numbers are numbers that have both a real and an imaginary part. They are typically written in the form a + bi, where a is the real part and bi is the imaginary part (b is a real number and i is the imaginary unit).

Why do we need complex numbers?

Complex numbers are useful for solving problems that involve square roots of negative numbers, such as in electrical engineering, physics, and other scientific fields. They also have many applications in mathematics, including in the study of polynomials and equations.

How do you add and subtract complex numbers?

To add or subtract complex numbers, simply combine the real parts and the imaginary parts separately. For example, (3 + 4i) + (2 + 6i) = (3 + 2) + (4 + 6)i = 5 + 10i. Similarly, (3 + 4i) - (2 + 6i) = (3 - 2) + (4 - 6)i = 1 - 2i.

How do you multiply and divide complex numbers?

To multiply complex numbers, use the FOIL method (First, Outer, Inner, Last) and simplify. For example, (3 + 4i) * (2 + 6i) = 6 + 18i + 8i + 24i^2 = 6 + 18i + 8i + (-24) = -18 + 26i. To divide complex numbers, multiply the numerator and denominator by the conjugate of the denominator and simplify.

How are complex numbers represented on a graph?

Complex numbers are represented on a graph using the complex plane, which has the real numbers as the x-axis and the imaginary numbers as the y-axis. The point (a, bi) on the complex plane represents the complex number a + bi. The distance from the origin to the point is called the magnitude or modulus, and the angle formed by the point with the positive real axis is called the argument or phase angle.

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