The complex numbers $z$ and $w$ satisfy $|z| = |w| = 1$ and $zw \ne -1.$ (a) Prove that $\overline{z} = \frac{1}{z}$ and $\overline{w} = \frac{1}{w}.$ (b) Prove that $\frac{z + w}{zw + 1}$ is a real number.

it is contrapositive

i could not see the question too well so check yourself again too . this is because i want you to get it correct.

the answer is:

the correct option:

b.

to solve the problem, we need to remember how to operate to simplify exponential expressions using the logarithms.

we are given the equation:

then, using placing logarith with base 7 on both sides of the equation, we have:

so, rounding the obtained result to two decimal places (nearest hundreth), we have:

hence, we have that the correct option:

b.

have a nice day!