Complex Number Calculator

Complex number operations include: addition, subtraction, multiplication and division.

Complex number addition is performed according to the following rules: Let z1=a+bi, z2=c+di be any two complex numbers, then their sum is (a+bi)+(c+di)=(a+c)+(b+d)i.

The multiplication of complex numbers is stipulated to be carried out according to the following rules: Let z1=a+bi, z2=c+di (a, b, c, d∈R) be any two complex numbers, then their product (a+bi)(c+di)=(ac-bd)+(bc+ad)i.

Division operation rules:

Let the complex number a+bi(a, b∈R), divided by c+di(c, d∈R), its quotient is x+yi(x, y∈R), that is, (a+bi)÷

(c+di)=x+yi

∵(x+yi)(c+di)=(cx－dy)+(dx+cy)i.

∴(cx－dy)+(dx+cy)i=a+bi.

From the definition of complex number equality, we know that cx-dy=a dx+cy=b

Solve this system of equations and get x=(ac+bd)/(c^2+d^2) y=(bc-ad)/(c^2+d^2)

So: (a+bi)/(c+di)=(ac+bd)/(c^2+d^2) +(bc-ad)/(c^2+d^2)i