They aren't showing all their steps.gtg177i said:Homework Statement
z+(conjugate of z)^2=4
Homework Equations
z = x+iy
(x+iy)+(x-iy)^2=4
The Attempt at a Solution
the solutions give (x+iy)+(x-iy)^2= x + x^2 - y^2. how do they reach that?
gtg177i said:I get (x+iy)+(x-iy)^2 = x + iy + x^2 -2xiy + i^2*y^2.
I think the question is the ( conjugate of z )^2. e.g. z with the line on top of it and that squared.
Thanks!
Complex numbers are numbers that consist of 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 represented by the square root of -1, also known as i.
To add or subtract complex numbers, you simply add or subtract the real parts and the imaginary parts separately. For example, (3 + 2i) + (5 + 4i) = (3 + 5) + (2i + 4i) = 8 + 6i.
The conjugate of a complex number is when the sign of the imaginary part is changed. For example, the conjugate of 3 + 4i is 3 - 4i. This is important when dividing complex numbers.
To multiply complex numbers, you use the FOIL method (First, Outer, Inner, Last). For example, (3 + 2i)(5 + 4i) = 15 + 12i + 10i + 8i^2 = 7 + 22i. To divide complex numbers, you multiply the numerator and denominator by the conjugate of the denominator and simplify.
The absolute value of a complex number is the distance of the number from the origin on the complex plane. It is calculated by taking the square root of the sum of the squares of the real and imaginary parts. For example, the absolute value of 3 + 4i is √(3^2 + 4^2) = √25 = 5.