a, x, y, z are real numbers such that:
Using the identity, a =
show that:
thanks
Let , and similarly and . Then u, v, w all have absolute value 1, so their inverses are equal to their complex conjugates: (and similarly for v and w).
Now show that . But , with similar expressions for wu and uv. Deduce that . But a, on the left side of that equation, is real, so the imaginary part of the right side of the equation must be zero.