Write \(f(z)=2z+\bar z\) as \(u+iv\) with \(z=x+iy\).

Study Complex analysis in ZWMath →

Review the concept: Complex function

A rule \(f\) assigning to each \(z=x+iy\) of a set \(D\subseteq\mathbb{C}\) a unique complex number \(w=u+iv\); \(u\) and \(v\) are its real and imaginary parts.

More practice problems: complex function

• ZW-COMPLEX-FUNCTION-001 If f(z)=z^2, compute f(1+2i).
• ZW-COMPLEX-FUNCTION-002 For f(z)=z^2 with z=x+iy, what is the real part u(x,y)?
• ZW-COMPLEX-FUNCTION-003 For f(z)=z^2 with z=x+iy, what is the imaginary part v(x,y)?
• ZW-COMPLEX-FUNCTION-005 If f(z)=1/z, compute f(1+i).
• ZW-COMPLEX-FUNCTION-006 What is the natural domain of f(z)=(1)/(z-i)?
• ZW-COMPLEX-FUNCTION-007 For f(z)=|z|^2, compute f(3+4i).
• ZW-COMPLEX-FUNCTION-008 If f(z)=z^3, compute f(1+i).
• ZW-COMPLEX-FUNCTION-009 The function f(z)=z^2 maps the circle |z|=2 onto…

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