SOLUTION: z= (3+4i)(12-5i)/(2+i) a. |z| ? b. Re (z) and Im (z)? I doubt ! thnx alot

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: z= (3+4i)(12-5i)/(2+i) a. |z| ? b. Re (z) and Im (z)? I doubt ! thnx alot       Log On


   

Question 915479: z= (3+4i)(12-5i)/(2+i)
a. |z| ?
b. Re (z) and Im (z)?
I doubt !
thnx alot
Answer by tommyt3rd(5050) About Me  (Show Source):
You can put this solution on YOUR website!
Expanding the numerator

z=+%28%283%2B4i%29%2812-5i%29%29%2F%282%2Bi%29=%2836-15i%2B48i-20i%5E2%29%2F%282%2Bi%29+

z=%2856%2B33i%29%2F%282%2Bi%29=%28%2856%2B33i%29%282-i%29%29%2F%282%5E2%2B1%5E2%29

z=%28112-56i%2B66i-33i%5E2%29%2F5=%28145%2B10i%29%2F5

z=29%2B2i

abs%28z%29=sqrt%2829%5E2%2B2%5E2%29=13sqrt%285%29
Re%28z%29=29
Im%28z%29=2