$\displaystyle a, b, c, d$ are real numbers.

When they satisfy the equations $\displaystyle a^2+b^2=1$, $\displaystyle c^2+d^2=1$, $\displaystyle ac+bd=0$, find the value of $\displaystyle ab+cd$.

I got as far as getting $\displaystyle a^2+c^2=1$, but I can't seem to go any further.

Please help.