Question

If z and ω are two non-zero complex numbers such that |zω| = 1 and Arg(z) – Arg(ω) = `π/2`, then `barzω` is equal to ______.

Options

• –1

• 1

• –i

• i

Answer 1

If z and ω are two non-zero complex numbers such that |zω| = 1 and Arg(z) – Arg(ω) = `π/2`, then `barzω` is equal to –1.

Explanation:

`|barzω| = |barz||ω|`

= |z||ω|

= |zω|

= 1   ...`[∵ |barz| = |z|]`

`"Arg"(barzω) = "arg"(barz) + "arg"(ω)`

= –arg(z) + arg ω

= `-π/2`  ...`[∵ "arg"(barz) = -"arg"(z)]`

∴ `barzω` = –1