Complex Numbers

A number of the form a + ib, where a and b are real numbers and , is defined as a complex number. For the complex numbers z = a + ib, a is called the real part (denoted by Re z) and b is called the imaginary part (denoted by Im z) of the complex number z.

Example: For the complex number , Re and Im

Two complex numbers z1 = a + ib and z2 = c + id are equal if a = c and b = d. Modulus of a Complex NumberThe modulus of a complex number z = a + ib, is denoted by , and is defined as the non-negative real number , i.e., .

Example 1: If z = 2 – 3i, then

Conjugate of Complex NumberThe conjugate of a complex number z = a + ib, is denoted by , and is defined as the complex number a – ib, i.e., .

Example 2: Find the conjugate of .

Solutio…

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