Problem on Polar Form of Complex Number

TL;DR

Learn how to convert a complex number from Cartesian form to polar form using the standard form and formulas for modulus and argument.

Transcript

hello students so in the last video we have seen the concept of polar form and how to find the argument of any given complex number and now in this video we are gonna see a numerical based on that concept where we'll apply those formula over here to get the solution so now here we have to express 1 plus 2i upon 1 minus 3i in the form of r into cos ... Read More

Key Insights

• 💁 Converting a complex number from Cartesian to polar form involves bringing it to standard form, eliminating the complex number from the denominator, and dividing the numerator separately.
• ❎ The modulus of a complex number is found using the formula square root of (real part squared + imaginary part squared).
• 😇 The argument of a complex number is found using the formula tan inverse (imaginary part / real part) and considering the correct quadrant.
• 😑 Complex numbers can be expressed in polar form as r(cos(theta) + i sin(theta)), where r is the modulus and theta is the argument.
• 😌 It is important to understand the rules for finding the argument based on the quadrant the complex number lies in.
• #️⃣ Problems involving converting complex numbers to polar form can vary in numbers and quadrants.
• 🎁 Understanding the concept and formulas presented in the video is crucial for solving similar problems in the examination.

Questions & Answers

Q: What is the first step to convert a complex number from Cartesian to polar form?

The first step is to bring the complex number to standard form, where it has a single real part and a single imaginary part in the form of x + iy.

Q: How do we eliminate the complex number from the denominator?

To eliminate the complex number from the denominator, we take its conjugate and multiply it with both the numerator and denominator.

Q: How do we find the modulus of the complex number?

The modulus is found by taking the square root of the sum of the squares of the real part and the imaginary part of the complex number.

Q: How do we find the argument of the complex number?

The argument is found using the formula tan inverse (imaginary part / real part). The correct quadrant for the number must also be considered.

Summary & Key Takeaways

• The video explains how to convert a complex number from Cartesian form to polar form by bringing it to standard form.

• To eliminate the complex number from the denominator, the conjugate of the complex number is taken and multiplied with the numerator and denominator.

• After simplification and division, the complex number is converted to the polar form by finding the modulus and argument.