# Can someone help me with this question for complex analysis?!

• May 25th 2009, 08:18 AM
NaNa
Can someone help me with this question for complex analysis?!
1) A liner mapping maps the point (1+i) onto (6+5i) and the point (1-i) onto (4+i). Find this linear mapping and any fixed points associated with it.

Can I found somewhere some good nodes for complex analysis becuase I m really confuse.(Thinking)

Thanks a lot!(Smile)
• May 25th 2009, 09:39 AM
shawsend
How about using determinants to solve for a and b in the equation:

$w=za+b$

You got two points, two equations, two unknowns right?

Then solve for the fixed points:

$z=za+b$
• May 25th 2009, 09:47 AM
NaNa
Oh now is clear many thanks!
• May 25th 2009, 12:38 PM
HallsofIvy
Quote:

Originally Posted by NaNa
1) A liner mapping maps the point (1+i) onto (6+5i) and the point (1-i) onto (4+i). Find this linear mapping and any fixed points associated with it.

Can I found somewhere some good nodes for complex analysis becuase I m really confuse.(Thinking)

Thanks a lot!(Smile)

A linear function must be of the form f(z)= az+ b. Since it maps 1+ i onto 6+_5i, 6+ 5i= a(1+ i)+ b and since it maps 1- i onto 4+ i, 4+ i= a(1- i)+ b. That gives you two equations to solve for a and b.