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

Find free revision notes of Complex Numbers in this article. All important formulae and terms are included in this revision notes.

Created On: 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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Collinearity

       Complex Number

Circle

  • 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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