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Blinding irritant, please help

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Blinding irritant, please help

we know: a*a + b*b = 1, c*c + d*d = 1, a*c - b*d = 1/2.
Required yo find a*d + b*c

Hi there,

The question was in no way homework, I'm way past that age. I happened to see the problem on the webb and I got stuck, but if, as your notice seems to imply the problem was too easy for you lot. Rest assured I will not bother you any further.

Apologies for misjudging.
If you see the first equation, you notice that a+ib is a complex number of modulus 1; equivalently, a and b are cosine and sine of some angle theta. Second equation says similar of c+id.
But then, what are ac-bd and ad+bc?

We are really not into doing other people's homework.
I suppose you have already done some trigonometry, or some algebra in the complex plane?

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