Evaluating Im (z*w)/(2z-3w) for z=3-i and w=1+3i

[geffman1]

hey guys I've got a problem

If z = 3− i and w = 1+3i, evaluate Im (z∗w)/(2z − 3w)


my attempt... ill do top first (3+i)(1+3i)=3+9i+i+3i^2=10i?

bottom=3-2i-3+9i=7i therefore answer equals 10/7 however answer is 3/13. could someone please help. thanks

 

[rock.freak667]

(3-i)(1+3i) is the numerator, work that out again.

Also for 2z, why did you have 3-2i instead of 2(3-i)=6-2i ?

 

[geffman1]

o soz that * is not a multiple sign its the conjurate sign i think. o yeh the bottom should be (6-2i)-(3+9i)=3+7i. is that right??

 

[Cyosis]

No [itex]-2i-9i \neq -7i[/itex]. The numerator has been calculated correctly.