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Polar Representation of a Complex Number- 1 Video Lecture | Mathematics (Maths) for JEE Main & Advanced
FAQs on Polar Representation of a Complex Number- 1 Video Lecture - Mathematics (Maths) for JEE Main & Advanced
| 1. What is the polar representation of a complex number? |  |
Ans. The polar representation of a complex number is a way to express a complex number in terms of its magnitude and angle. It is represented as r(cosθ + isinθ), where r is the magnitude or modulus of the complex number, and θ is the angle or argument of the complex number.
| 2. How do you convert a complex number to polar form? | |
Ans. To convert a complex number to polar form, you can use the following steps:
1. Find the magnitude (r) of the complex number using the formula r = √(real^2 + imaginary^2).
2. Find the angle (θ) of the complex number using the formula θ = atan2(imaginary, real).
3. Write the complex number in polar form as r(cosθ + isinθ).
| 3. How do you convert a complex number in polar form to rectangular form? | |
Ans. To convert a complex number in polar form to rectangular form, you can use the following steps:
1. Identify the magnitude (r) and angle (θ) of the polar form.
2. Use the formula real = r * cos(θ) to find the real part.
3. Use the formula imaginary = r * sin(θ) to find the imaginary part.
4. Write the complex number in rectangular form as real + imaginaryi.
| 4. What is the significance of the angle in the polar representation of a complex number? | |
Ans. The angle in the polar representation of a complex number represents the direction or orientation of the complex number in the complex plane. It provides information about the phase or rotation of the complex number. The angle is important in understanding the behavior of complex numbers in various mathematical operations, such as multiplication, division, and exponentiation.
| 5. How do you find the principal argument of a complex number in polar form? | |
Ans. The principal argument of a complex number in polar form is the principal value of its angle, which lies between -π and π. To find the principal argument, you can use the atan2 function in most programming languages, which takes the imaginary and real parts of the complex number as inputs and returns the angle in the desired range.
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