- #1
blckndglxy
- 2
- 0
Homework Statement
Given that a complex number z and its conjugate z¯ satisfy the equation z¯z¯ + zi = -i +1. Find the values of z.
blckndglxy said:Homework Statement
Given that a complex number z and its conjugate z¯ satisfy the equation z¯z¯ + zi = -i +1. Find the values of z.
Homework Equations
The Attempt at a Solution
You are not right, z.z- = |z|2, square of the magnitude of z. zi is z multiplied by i.Bibatshu Thapa said:Hey, I think z.z-=1 but what's with the zi thing. Can you upload the picture of your question? Its not clear enough.
hello there.. so z¯ = x-iy right? so i have to replace the z¯ too right? sorry I'm still new and I'm clueless with this question..ehild said:Hi blckndglxy, welcome to PF.
You have to show some attempt at solving the problem. Write z as z=x+iy, substitute into the equation z¯z¯ + zi = -i +1 and solve.
Yes. Replace z with x+iy and z- with x-iy.blckndglxy said:hello there.. so z¯ = x-iy right? so i have to replace the z¯ too right? sorry I'm still new and I'm clueless with this question..
Writing ##z = x+iy## and ##bar{z} = x - iy##, your equation becomesblckndglxy said:hello there.. so z¯ = x-iy right? so i have to replace the z¯ too right? sorry I'm still new and I'm clueless with this question..
The original equation is z¯z¯ + zi = -i +1. z¯z¯ is not |z|2,Ray Vickson said:Writing ##z = x+iy## and ##bar{z} = x - iy##, your equation becomes
$$|z|^2 = 1 - i - zi$$.
Thanks a lot. Well I had forgotten the fact you mentioned. Really HELPFUL!ehild said:Hi blckndglxy, welcome to PF.
You have to show some attempt at solving the problem. Write z as z=x+iy, substitute into the equation z¯z¯ + zi = -i +1 and solve.
A complex number is a number that contains both a real and an imaginary part. It is written in the form a + bi, where a is the real part and bi is the imaginary part with the imaginary unit i.
The conjugate of a complex number a + bi is the complex number a - bi. This means that the sign of the imaginary part is changed. For example, the conjugate of 3 + 4i is 3 - 4i.
To find the conjugate of a complex number, simply change the sign of the imaginary part. If the imaginary part is positive, make it negative and if it is negative, make it positive.
The conjugate is important in complex number problems because it allows us to simplify and manipulate complex numbers in order to solve equations and perform operations. It also helps us find the magnitude and angle of a complex number in polar form.
To divide complex numbers, we use the conjugate of the denominator to rationalize the expression. This means that we multiply both the numerator and denominator by the conjugate of the denominator. This will eliminate the imaginary part in the denominator, making it easier to perform division.