1) how to graph |z+6| >= |z|

2) f(z) = x^2 + i y^2

assume Cauchy-Riemann equation

ux = vy and uy = -vx

are satisfied for f(z)

where z = x + iy and u(x,y) = x and v(x,y) = y

find all values of z which satisfy C-R on f(z)

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I've can sketch |z=4| and |z| individually but how to put them together and which portion to shade?

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I started 2 with

u(x,y) = x^2 and v(x,y) = y^2

ux = 2x and uy = 2y

so 2x = 2y => x = y

also uy = - vx

so 0 = 0

hence, z = x+iy = x + ix = y + iy

but when i put x = y in f(z) i get

f(z) = x^2 + ix^2 = y^2 + iy^2

but this f(z) does not satisfy C-R equations.