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JEE Main Mathematics

Complex Numbers and Quadratic Equations

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Complex numbers in the Argand plane with their modulus and argument, and quadratic equations: their roots, the relations to the coefficients and the nature of the roots.

Key formula
x=−b±b2−4ac2a,α+β=−ba,αβ=ca,∣a+ib∣=a2+b2x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, \quad \alpha + \beta = -\frac{b}{a}, \quad \alpha\beta = \frac{c}{a}, \quad |a + ib| = \sqrt{a^2 + b^2}

What this unit covers

  • Complex numbers as ordered pairs of reals

  • Representation of complex numbers in the form a + ib and their representation in a plane, Argand diagram

  • Algebra of complex numbers

  • Modulus and argument (or amplitude) of a complex number

  • Quadratic equations in real and complex number systems and their solutions

  • Relations between roots and coefficients, nature of roots

  • The formation of quadratic equations with given roots

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