Find Re f and Im f fz 4z2 3z i 1Solutionz xiy So we can

Find Re f and Im f: f(z) = 4z^2 + 3z + i - 1

z = x+iy

So, we can get

f(z) = 4(x+iy)^2 +3(x+iy) +i-1

Simplifying this,

f(z) = 4x^2 - 4y^2 + 8ixy + 3x + 3iy +i-1

Now taking all with i together and rest together,

f(z) = 4x^2 - 4y^2 + 3x -1 +i(8xy+3y+1)

So, considering this,

Real f = 4x^2 - 4y^2 + 3x-1

Im f = 8xy+3y+1