## Product to Sum Formulas | Trigonometry

Product to sum formulae are used to represent multiplication of sine and cosine of angles as sum of the sine and cosine functions. These formulae are quite useful when solving trigonometric integrals like…

## Simplify Powers of Imaginary Number iota

Firstly let’s have a look at what’s general rule for simplifying powers of Complex Numbers.Below is a brief summary of what’s that rule is? Firstly dividing power of iota by 4 Then write…

## Prove that Modulus of a Complex Number and it’s Conjugate are Same

For any Complex Number let’s say z => The Modulus of it and it’s conjugate will be equal. This means that |z| = |z̄| holds true for any Complex Number.Let’s now see Mathematical… ## Chapter 5 Complex Numbers and Quadratic Equations Solutions – NCERT Class 11 Mathematics

Exercise 5.1 Express each of the complex numbers given in the Exercises 1 to 10 in the form a + ib As (5i)(- 3i/5) just simplifies to 3 which is just a Real… ## Miscellaneous Exercise Complex Numbers and Quadratic Equations – NCERT Class 11 Mathematics Chapter 5

1. Evaluate [i18 + (1/i)25]3 Let’s simplify this equation 2. For any two complex numbers z1 and z2, prove that Re(z1 z2) = Re(z1) Re(z2) – Im(z1) Im(z2) Let’s suppose thatz1 = a… ## Exercise 5.3 Solutions Complex Numbers and Quadratic Equations – NCERT Class 11 Mathematics Chapter 5

Solve each of the following equations: 1. x2 + 3 = 0 x2 + 3 = 0 x2 = – 3 x = ± √-3 This can be rewritten as followingx = ±… ## Exercise 5.2 Solutions Complex Numbers and Quadratic Equations – NCERT Class 11 Mathematics Chapter 5

Find the modulus and the arguments of each of the complex numbers in Exercises 1 to 2. 1. z = – 1 – i √3 Any Complex Number of form z = a…

## Exercise 5.1 Question Number 14 – Class 11 Maths NCERT Solution

14. Express the following expression in the form of a + ib : (3 + i√5)(3 – i√5)/[(√3 + √2i) – (√3 – i√2)] Thus (3 + i√5)(3 – i√5)/[(√3 + √2i) –… 