If z=cosθ+i sinθthen (z^2+z)= (a) (3 θ/ 2) (b) θ(c) (θ/ 2) (d) 3 θ

Name: Problem 141, Chapter 2: JEE Maths
Uploaded: 2021-08-22T06:27:08-08:00
Duration: 2 min 17 s
Channel: Gaurav Kalra
Description: If z=cosθ+i sinθthen (z^2+z)= (a) (3 θ/ 2) (b) θ(c) (θ/ 2) (d) 3 θ

step 1 I have given here z is cost theta plus iota sine theta i need to find out arguments z squared so

If z=cosθ+i sinθthen (z^2+z)= (a) (3 θ/ 2) (b) θ(c) (θ/ 2)...

Key Concepts

Argument of a Complex Number

The argument refers to the angle a complex number makes with the positive real axis in the complex plane. It is a crucial concept for determining the direction or phase of a complex number and is especially useful when performing operations in polar form.

Exponentiation in Polar Form

When a complex number in polar form is raised to a power, its modulus is raised to that power and its argument is multiplied by that power. This property, often referred to as De Moivre's theorem, simplifies the computation of powers and roots of complex numbers.

Polar Form Representation

This concept involves expressing complex numbers in the form r(cos ? + i sin ?) or equivalently re^(i?), where r is the modulus and ? is the argument. It simplifies operations such as multiplication, division, and raising to a power, by allowing the separation of magnitude and angle components.

Complex Conjugate

The complex conjugate of a complex number, given by changing the sign of the imaginary part, reflects the number across the real axis in the complex plane. Understanding the role of the complex conjugate is important when computing sums or products that involve a number and its conjugate.

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