(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Express [tex]cos^{-1}(x+iy)[/tex] in the form [tex]A+iB[/tex]).

3. The attempt at a solution

[tex]x+iy=cos(a+ib)[/tex]

[tex]x-iy=cos(a-ib)[/tex]

[tex]2x=2cos(a)cosh(b)[/tex]

[tex]x=cosa coshb[/tex]

Similarly,

[tex]y=-sina sinhb[/tex]

Using these values, I got [tex]x^2+y^2=cos^2a +sinh^2b[/tex], but I dont know where to go from here.

Alternatively,

[tex]a+ib=cos^{-1}(x+iy)[/tex]

[tex]a-ib=cos^{-1}(x-iy)[/tex]

[tex]2a=cos^{-1}(x^2+y^2 -\sqrt{1-(x+iy)^2}\sqrt{1-(x-iy)^2})[/tex]

and similarly,

[tex]2b=cos{-1}(x^2+y^2+\sqrt{1-(x+iy)^2}\sqrt{1-(x-iy)^2}[/tex],

but after expanding, these expressions are too complex. Is this the final expression though? I dont have the answer, so I have nothing to compare this to.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Complex Numbers homework

**Physics Forums | Science Articles, Homework Help, Discussion**