The following properties of complex numbers are helpful to better understand complex numbers and also to perform the various arithmetic operations on complex numbers.
Conjugate of a Complex Number
The conjugate of the complex number is formed by taking the same real part of the complex number and changing the imaginary part of the complex number to its additive inverse. If the sum and product of two complex numbers are real numbers, then they are called conjugate complex numbers. For a complex number z = a + ib, its conjugate is ¯zz¯ = a – ib.
The sum of the complex number and its conjugate is z+¯zz+z¯ = ( a + ib) + (a – ib) = 2a, and the product of these complex numbers z.¯zz.z¯ = (a + ib) × (a – ib) = a2 + b2.
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