I need help with this problem, I'm very confused

Prove that for all complex numbers z and w:

1. zw* + z*w is always real

2. zw* - z*w is purely imaginary or zero.

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- January 9th 2010, 10:39 AMerickvm123Proving complex numbers
I need help with this problem, I'm very confused

Prove that for all complex numbers z and w:

1. zw* + z*w is always real

2. zw* - z*w is purely imaginary or zero. - January 9th 2010, 11:55 AMAmer