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The division of two complex numbers can be accomplished by multiplying the numerator and denominator by the complex conjugate of the denominator, for example, with z_1=a+bi ...

The unique nonnegative square root of a nonnegative real number. For example, the principal square root of 9 is 3, although both -3 and 3 are square roots of 9. The concept ...

A graph G whose line graph is L(G) is called the root graph R(L(G)) of L(G). In order words, R(L(G))=G. The root graph of a connected graph is unique except for K_3=C_3 (the ...

The sum of the reciprocals of roots of an equation equals the negative coefficient of the linear term in the Maclaurin series.

Complex Analysis

A complex polynomial is a polynomial with complex coefficients.

A function whose range is in the complex numbers is said to be a complex function, or a complex-valued function.

Complex analysis is the study of complex numbers together with their derivatives, manipulation, and other properties. Complex analysis is an extremely powerful tool with an ...

Let z=x+iy and f(z)=u(x,y)+iv(x,y) on some region G containing the point z_0. If f(z) satisfies the Cauchy-Riemann equations and has continuous first partial derivatives in ...

A complex translation is a map of the form z|->z+a, where a is a fixed complex number, which corresponds to translation (shifting) of points the complex plane by the complex ...