Thread: 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.

Thanks a lot!

How about using determinants to solve for a and b in the equation:



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

Then solve for the fixed points:

Oh now is clear many thanks!

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.

Thanks a lot!

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.