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Complex Number: Quick Revision of Formulae for IIT JEE, UPSEE & WBJEE

Dec 27, 2016 15:27 IST

    Find Mathematics Quick Revision notes of the unit Complex Numbers. This quick revision notes provide complete formulae and important terms in Complex Number. Approximately 2-3 questions are asked in any engineering entrance exam from this chapter.

    This revision notes is very important for UPSEE/UPTU and WBJEE exams where questions are asked directly on the basis of formulae.

    Also, when exams are round the corner then it is not possible to revise complete books so we have come up with unit wise formulas and important terms. Once you have gone through chapters thoroughly and understood it well there is no need to study it again and again. You can only revise important formulas and terms which will save your precious time.

    Complex Numbers

    • z  = a + ib, where a, b are real numbers

                a is called the real part of z

                b is called the imaginary part of z

    • i2 = −1, i is called iota
    • i3 = i2.i = −i, i4 = i2.i 2= 1, i5 = i3.i 2= i, i6 = i4.i2 = −1
    • If Re (z) = 0 and Im(z) ≠ 0, then z is said to be purely imaginary.
    • If Im(z) = 0, then z is said to be purely real.

    If z1  = a + ib and z2  = c + ib, then

         Complex Number

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    Polar Form

           Complex Number

    Complex conjugate

            Complex Number

    Angle between two line segments

            Complex Number

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           Complex Number


    • Equation of circle is given as:

              Complex Number

                where, a = centre of the circle, r = radius of the circle

    Equilateral Triangle

    • If P, Q and R are vertices of an equilateral triangle representing the complex numbers z1, z2and z3 respectively, then z1z2z3 + z1z2z3 + z1z2z3 = z12 + z22 + z32

    DeMoivre's Theorem

           Complex Number

    Cube root of Unity

    • Let n be a positive integer, then the roots of the equation z3 = 1is called cube root of unity.       

          Complex Number

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