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…

Read moreFirstly 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…

Read moreFor 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…

Read moreExercise 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…

Read more1. 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…

Read moreSolve each of the following equations: 1. x2 + 3 = 0 x2 + 3 = 0 x2 = – 3 x = ± √-3 This can be rewritten as followingx = ±…

Read moreFind 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…

Read more14. 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) –…

Read more13. – i Multiplicative Inverse of any Complex Number of form a + ib is equals to 1/a + ib⇒ Multiplicative inverse of – i is equals to 1/- i Thus Multiplicative Inverse…

Read more12. √5 + 3i Multiplicative Inverse of any Complex Number of form a + ib is equals to 1/a + ib⇒ Multiplicative inverse of √5 + 3i is equals to 1/(√5 + 3i)…

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