- #1

shannon

- 11

- 0

## Homework Statement

Show that the vector z

_{1}is parallel to z

_{2}if and only if Im(z

_{1}z

_{2}*)=0

note: z

_{2}* is the complement of z

_{2}

## Homework Equations

## The Attempt at a Solution

I would probably convert z to polar form.

so, z

_{1}=r

_{1}(cos Ѳ

_{1}+isin Ѳ

_{1})

z

_{2}=r

_{2}(cos Ѳ

_{2}+isin Ѳ

_{2})

so, z

_{2}*=r

_{2}(cos Ѳ

_{2}-isin Ѳ

_{2})

Then, I would plug it into Im(z

_{1}z

_{2}*)=0

so, Im(r

_{1}(cos Ѳ

_{1}+isin Ѳ

_{1})r

_{2}(cos Ѳ

_{2}-isin Ѳ

_{2}))

which is: r

_{1}r

_{2}sin Ѳ

_{2}sin Ѳ

_{2}

But I'm not sure where to go from here...

PLEASE HELP!