Prove that if $w, z$ are complex numbers such that $|w|=|z|=1$ and $wz\ne -1$, then $\frac{w+z}{1+wz}$ is a real number.

See proof below

Step-by-step explanation:

Let . If w=-z, then r=0 and r is real. Suppose that w≠-z, that is, r≠0.

Remember this useful identity: if x is a complex number then where is the conjugate of x.

Now, using the properties of the conjugate (the conjugate of the sum(product) of two numbers is the sum(product) of the conjugates):

=

Thus . From this, . A complex number is real if and only if it is equal to its conjugate, therefore r is real.

how long did the flood last

step-by-step explanation:

then i will answer