Help needed to calculate charactersitc impedence

[crazybilal]

I am really stuck in calculating characteristic impededence. Can some one help me .
Here is the data
L=0.2microhenry/meter
c=300 picofarad/meter
r= 5 ohm /meter
g=o.ooq mho/meter
f = 500 mhz

Zo=sqrt((r+jwl)/(g+jwc))

answer should be

25.8+0.03j

but how?

 

[WimRFP]

convert micro and pico to 10^-6 and 10^-12

Multiply your expression for Z0 with (g-wjc)/(g-jwc).

As (g+jwc)*(g-jwc) = g^2+(wc)^2, the denominator becomes a real number.

Other path can be convert both numerator and denominator to polar notation (modulus/argument). Division simplifies to division of moduli and subtraction of arguments.

Convert the polar result back to cartesian result.