SOLUTION: Any help would be appreciated with this. If s and t are two complex numbers, prove the following. a) |s+t|^2=|s|^2+|t|^2+(st*+s*t) |s|^2+|t|^2+(st*+s*t) =ss*+tt*+st*+s*

Algebra.Com
Question 979594: Any help would be appreciated with this.
If s and t are two complex numbers, prove the following.
a) |s+t|^2=|s|^2+|t|^2+(st*+s*t)

|s|^2+|t|^2+(st*+s*t)
=ss*+tt*+st*+s*t
Using s=a+bi and t=c+di
=a^2+b^2+c^2+d^2+2ac+2bd

|s+t|^2 = a^2+2abi-b2+2ac+2bci+2adi-2bd+c^2+2cdi-d^2
Which seems quite wrong.
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
If s and t are two complex numbers, prove the following.
|s+t|^2 = a^2+2abi-b2+2ac+2bci+2adi-2bd+c^2+2cdi-d^2
You did that wrong.  add s=a+bi and t=c+di before you find the magnitude
or absolute value:

|s+t|² = |(a+bi)+(c+di)|² = |(a+c)+(b+d)i| = (a+c)²+(b+d)² = 

a²+2ac+c²+b²+2bd+d² 

Then when you do the other side:

|s|²+|t|²+(st*+s*t) = a²+b²+c²+d²+(a+bi)(c-di)+(a-bi)(c+di) = 

a²+b²+c²+d²+ac-adi+bci+bd+ac+adi-bci+bd = a²+b²+c²+d²+2ac+2bd

and they are equal.

Edwin
RELATED QUESTIONS

could i get some help with this? (a) Find the point of intersection between the... (answered by Fombitz)
I'm needing some help with the following problem. Perform the indicated operation and... (answered by feliz1965)
Completely factor the following: r(s) = 2s2 + st – 2s + t @ Normally, this would be... (answered by Edwin McCravy)
Hello. I'm needing some help with checking what I did wrong on this problem: Perform... (answered by josmiceli)
Multiply (s+t)(s^2-st+t^2) Thank you (answered by Fombitz)
Hi, I'm having a difficult time solving the following problem: Point P lies on... (answered by ewatrrr)
If an object is projected vertically upward from an altitude of s(o) feet with an intial... (answered by nerdybill)
If r,s, and t are integers greater than 1, where rs = 15 and st = 33, which of the... (answered by Edwin McCravy)
Completely factor the following: r(s) = 2s^2 + st – 2s + t @ Normally, this would be... (answered by checkley77)