| Published | 2022-05-02 |
| Platform | Udemy |
| Number of Students | 1 |
| Price | $39.99 |
| Instructors |
studi live
|
| Subjects |
IIT-JEE Main & Advanced | BITSAT | SAT | MSAT | MCAT | State Board | CBSE | ICSE | IGCSE
Complex Numbers and Quadratic Equations
Need for complex numbers, especially √1, to be motivated by inability to solve some of the quadratic equations
Algebraic properties of complex numbers
Argand plane and polar representation of complex numbers
Statement of Fundamental Theorem of Algebra
Solution of quadratic equations in the complex number system
Square root of a complex number
SUMMARY
1. A number of the form a + ib, where a and b are real numbers, is called a complex number, a is called the real part and b is called the imaginary part of the complex number.
2. Let z1 = a + ib and z2 = c + id. Then (i) z1 + z2 = (a + c) + i (b + d) (ii) z1 z2 = (ac – bd) + i (ad + bc)
2. The conjugate of the complex number z = a + ib, denoted by z̄ , is given by z̄ = a – ib.
3. The polar form of the complex number z = x + iy is r (cosθ + isinθ), where r = √(x2 + y2) (the modulus of z) and cosθ = x/r , sinθ = y/r . (θ is known as the argument of z. The value of θ, such that – π < θ ≤ π, is called the principal argument of z.
4. A polynomial equation of n degree has n roots.
5. The solutions of the quadratic equation ax2 + bx + c = 0, where a, b, c ∈ R.