Question

If (2i/2+i)-(3i/3+i)=a+bi, then b=

Answer 1

Answer:

b = -1/10.

Step-by-step explanation:

(2i/2+i)-(3i/3+i)

= 2i(3 + i) - 3i(2 + i) / (2 + i)(3 + i)

= 6i + 2i^2 - 6i - 3i^2 / (2 + i)(3 + i)

=  (-2 + 3) / (6 + 5i - 1)

= 1 / (5 + 5i)

Now we multiply top and bottom by 5 - 5i :

= 5 - 5i / (5 + 5i)(5 - 5i)

=  5 - 5i / 25 -25i^2

= 5 - 5i / 50

= 1/10 - 1/10i