Can You Solve This?

Test Preparation
1

<p>These problems have to do with the complex conjugates theorem.
x=r+si
z=u+vi
The conjugate of x=r-si
The conjugate of z=u-vi</p>

<p>1) Prove that the conjugate of (x+z)= the conugate of x plus the conjugate of z.
2) Prove that the conjucate of (xz)= the conugate of x times the conjuagte of z</p>

<p>Please explain your work as I am still not understanding how to find the conjucate of r+si+u+vi, in number 1.</p>

2

<p>I'll take a stab at it...</p>

<p>1) r+si+u+vi=r-si+u-vi
r's and u's cancel, leaving...
si+vi=-si-vi
2si=-2vi
si=-vi
Substituting back in...
r-vi+u+vi=r-(-vi)+u-vi
r+u=r+u</p>

<p>Not sure if this is right, but...yeah.</p>