Addition: let two complex numbers be a+bi and c+di, then their sum is (a+c)+(b+d) i. For example, if z 1=2+3i and z2=4+5i, then z1+z2 = (2+4)+.
Subtraction: Let two complex numbers be a+bi and c+di respectively, and their difference is (a-c)+(b-d) i. For example, if z 1=2+3i and z2=4+5i, then z1-z2 = (2-4)+.
Multiplication: let two complex numbers be a+bi and c+di respectively, and the product is (AC-BD)+(AD+BC) i. For example, if z 1=2+3i and z2=4+5i, then z1× z2 = (2× 4-3.
Division operation: Let two complex numbers be a+bi and c+di respectively, then their quotient is [(a+b )× (c-d)]/[(c+d )× (c-d)]+(b× d)/[(c+d )× (c-d)] i.
In addition, in the range of complex numbers, any non-zero complex number has only two square roots and is a pair of * * * yoke complex numbers. Let a nonzero complex number be r=cosθ+i sinθ (where r >；; 0), then its two square roots are √r=(cos(θ/2))+(sin(θ/2))i and-√ r = (cos (θ/2)-sin (θ/2)) i.
The above formulas are the basis of complex number operations, through which various complex number operations can be completed, including addition, subtraction, multiplication, division, square root and so on. These formulas are widely used in practical problems, such as circuit analysis, signal processing and other fields.