Thread: Another complex number problem.

Hello forumers,

While learning complex numbers, i got stuck in this two problems:

1. and , find if:

a) is imaginary number
b) is real number

2. Find if:

and .

Thank you.

3. . If and If find complex numbers z and w.

3.
z= a+ib, w=c+id

(1)
(2)

z+w=(a+c)+i(b+d)=i

so a+c=0 and b+d=1
so c=-a and d=1-b

so by (1) and (2)


and


solving for b;
b=-1

d=1-b=2

so a=1 or -1
c=-a=-1 or 1

so z=1-i, w=-1+2i or z=-1-i, w=1+2i

Thank you Krahl. I solved 2 remaining problems.

First problem solution is: and just for a).
Second problem solutions is:

If you have any questions about solution, feel free to ask!

Thank you.