Verify "Explicitly" 9.3: Zwiebach Page 159

[ehrenfest]

Homework Statement

Quick Calculation 9.3 asks us to verify "explicitly" that x^\mu(tau, sigma) is real. But can't you just look at 9.49 where this is quite manifest? What do they mean "explicitly"?

Homework Equations

The Attempt at a Solution

 

[Jimmy Snyder]

Explicitly doesn't mean much here. he simply means show that
$$(X^{\mu}(\tau,\sigma))^{*} = X^{\mu}(\tau,\sigma).$$
But then how else would you do it? As for using (9.49), the business end of the work is in showing that the expression inside the parentheses is imaginary. Since the same expression appears in (9.52) it hardly matters which one you use. However, if you use (9.49), you are not finished since all you will have proved is that the l.h.s. of that equation is real, not what was asked in the QC. But if you use (9.52) you are finished.