Can someone explain the property of complex conjugates in this equation?

Click For Summary
The equation z_1\bar{z_2} + \bar{z_1}z_2 = 2\:Re(z_1\bar{z_2}) illustrates the relationship between complex numbers and their conjugates. The left side represents the sum of the products of two complex numbers and their conjugates. The right side expresses this sum as twice the real part of the product of the two complex numbers. The original poster initially sought clarification but later confirmed understanding of the concept. This highlights the importance of complex conjugates in simplifying expressions involving complex numbers.
daster
Could someone please show me how:

z_1\bar{z_2} + \bar{z_1}z_2 = 2\:Re(z_1\bar{z_2})

where \bar{z} is the conjugate of z.
 
Mathematics news on Phys.org
Nevermind. I got it. :smile:
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
View full post »

Similar threads

MHB Finding Real Part of $z$ for Complex Numbers
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Expansion with respect to ##z_1##
  • · Replies 1 ·
Replies
1
Views
1K
High School Computing a tricky complex math problem - where did I go wrong?
  • · Replies 7 ·
Replies
7
Views
1K
MHB A complex numbers' modulus identity.
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Visualization of complex vectors and dot product
  • · Replies 14 ·
Replies
14
Views
4K
Undergrad How to Prove the Partial Fraction Formula for Distinct Complex Numbers?
  • · Replies 2 ·
Replies
2
Views
2K
MHB Ap1.3.51 are complex numbers, show that
  • · Replies 4 ·
Replies
4
Views
2K
Is the Max Function a Norm in R^3?
  • · Replies 6 ·
Replies
6
Views
2K
MHB A complex number problem that has been vexing me....
  • · Replies 2 ·
Replies
2
Views
2K
Least-square optimization of a complex function
  • · Replies 5 ·
Replies
5
Views
6K