Cartesian Coordinate System and Polar Coordinate System, Relationship between Cartesian coordinate system and polar coordinate system, Argand Diagram, Meaning of Modulus and Modulus of Complex Numbers mod(z)=|z|= r, Detailed explanation and derivation for argument of complex numbers arg(z), Polar form.

NCERT Exercise 5.2

Find the modulus and the arguments of each of the complex numbers in Exercises 1 to 2.

Question 1. \(z=-1-i \sqrt{3}\)

Question 2. \(z=- \sqrt{3}+i\)

Convert each of the complex numbers given in Exercises 3 to 8 in the polar form:

Question 3. \(1-i\)

Question 4. \(-1+i\)

Question 5. \(-1-i\)

Question 6. \(-3\)

Question 7. \(\sqrt{3}+i\)

Question 8. \(i\)