# CVFHF4

Find a function that is harmonic on the washer-shaped region between the circles with radii 1 and 2 and center (1,i). It should be 0 and 10 on the inner and outer circle.

Guess the answer $\phi(x,y) = A \mathrm{Log}|z-(1+i)|+B\,$.

At the point $i\,$, $A \mathrm{Log}|-1|+B=0 \implies B=0\,$

At the point $1-i\,$, $A \mathrm{Log}|-2i| = 10 \implies A=\frac{10}{\mathrm{Log}2}\,$

So the answer is

$\phi(z) = \frac{10}{\mathrm{Log}2} \mathrm{Log}|z-(1+i)| \,$.

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