Class 11 Math 2025 – Exercise 1.4
Topic: Cube Root and Fourth Root of Unity
Published by: www.mathuniverseonline.com
In Exercise 1.4 of the Class 11 Math 2025 syllabus, we explore two fascinating topics: the cube root of unity and the fourth root of unity. These concepts come from the chapter on complex numbers and are very important for students preparing for board exams. You’ll often find related questions in objective sections and short questions, so having a strong understanding is essential.
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This exercise is not about complicated mathematics. Instead, it focuses on simple ideas and patterns involving special complex numbers. The roots of unity are unique numbers that, when raised to a specific power (like 3 or 4), result in 1. Though they may sound tricky at first, the concepts are actually quite easy to grasp when explained in the right way.
What is the Cube Root of Unity?
The cube root of unity includes three special numbers. When each of these numbers is raised to the power of 3 (multiplied by itself three times), the result is 1. Out of the three, one is a regular real number (which you’re already familiar with), and the other two are complex numbers.
These numbers are not random. They follow a set of properties that make them very useful in algebra and exam problems. For example, their sum is zero, and multiplying them in a certain way also leads to interesting results. These properties are commonly tested in board exams, especially in multiple-choice or short-answer sections.
In our detailed video lecture, these properties have been explained in a simple, step-by-step manner. The goal is to make sure you don’t just memorize these roots but actually understand how they work. We’ve also covered a few important identities and proof-based properties that aren’t always fully explained in the textbook.
CHECK SOLUTION BELOW
Understanding the Fourth Root of Unity
Now, let’s move on to the fourth root of unity. As the name suggests, this includes four numbers. When each of these is raised to the power of 4, the result is again 1. Just like with the cube roots, one of these four is a real number, while the others are complex.
What’s interesting about the fourth roots is the geometrical pattern they form on the complex number plane. If you plot them, you’ll see a very symmetrical shape — which helps students visually understand the concept. This idea is not just helpful for math but also for visual learners who understand better with diagrams and shapes.
In our video lecture, we explain this geometric view in simple terms, making the topic even more interesting and easier to remember.
Why Is This Exercise Important?
You might wonder why roots of unity matter. Here's why:
They appear frequently in board exams, especially in short questions and MCQs.
They form the foundation for advanced concepts in complex numbers and algebra.
Their properties are easy to remember once properly explained.
Understanding them boosts your overall confidence in handling complex number problems.
If you’re aiming for good grades in your board exams, mastering this exercise is a smart move.
How We Teach It
At Math Universe by Sir Khawar, we believe in clear and practical explanations. Instead of overwhelming students with formulas, we focus on building the concept from the ground up. That’s why, in our video for Exercise 1.4, we’ve kept the approach:
Simple
Visual
Exam-focused
We’ve included short tricks, important identities, and side-by-side comparisons between cube and fourth roots to make learning faster and easier.
Need Full Step-by-Step Solutions?
If you’re looking for the complete solution to Exercise 1.4 — including written notes, solved identities, and extra practice — you can find everything you need on our website:
Visit: www.mathuniverseonline.com
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Final Tip
Don’t skip over this exercise thinking it’s minor. The cube root and fourth root of unity are short topics, but they often hold high value in exams. With a little effort, you can master them quickly and make sure you score well in both the short and objective parts of your test.
Start watching, start practicing — and take the next step towards exam success!
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