Complex numbers and quadratic equations Topics - IIT JEE Syllabus

1

2m1/10

📌 Key Formulaz = (a, b) = a + ib, a, b ∈ R

2

2m1/10

📌 Key Formulaz = a + ib, Re(z) = a, Im(z) = b

3

2m1/10

📌 Key FormulaArgand plane, (a, b) as coordinates of point representing z = a + ib

4

2m1/10

📌 Key FormulaGeometrical representation of complex numbers.

5

2m2/10

📌 Key FormulaAddition: (a+ib) + (c+id) = (a+c) + i(b+d), Multiplication: (a+ib)(c+id) = (ac - bd) + i(ad + bc)

6

2m3/10

📌 Key Formula|z| = √(a² + b²), arg(z) = θ such that tan θ = b/a

7

2m4/10

📌 Key Formula√(a + ib) = ±[√{(√(a²+b²) + a)/2} + i√{(√(a²+b²) - a)/2}]

8

2m3/10

📌 Key Formula|z₁ + z₂| ≤ |z₁| + |z₂|, |z₁ - z₂| ≥ ||z₁| - |z₂||

9

2m2/10

📌 Key Formulax = [-b ± √(b² - 4ac)] / 2a, For complex roots, they occur in conjugate pairs.

10

2m2/10

📌 Key FormulaSum of roots (α+β) = -b/a, Product of roots (αβ) = c/a

11

2m2/10

📌 Key FormulaDiscriminant D = b² - 4ac. D > 0: real and distinct, D = 0: real and equal, D < 0: complex conjugates.

12

2m2/10

📌 Key Formulax² - (sum of roots)x + (product of roots) = 0