For a real number b>0 and a real number x, define b^x, and show
Show that every complex number is the square of a complex number.
The second is a special case of the "fundamental theorem of algebra" but perhaps not as hard as I thought at first. Given any complex number a+ bi, write (x+ yi)^2= a+ bi. Multiply it out, equate real part to real part, and solve the two real number equations for x and y.