Exercise 1.1 Solution– First Year Math 2025 | Introduction to New Numbers
As students enter the world of intermediate mathematics, they encounter ideas that go beyond the numbers we've been using since primary school. One of these new ideas is introduced right at the start of the new First Year Mathematics 2025 syllabus — a unique kind of number that helps us solve problems we couldn't handle before. This number is part of a broader category known as complex numbers, and Chapter 1 is all about understanding what they are and why we need them.
Let’s take a look at the basics behind this fascinating concept — explained in a clear, non-technical way.
🌟 Why Learn About These New Numbers?
Sometimes in math, you come across problems that just don’t seem to have answers using regular numbers. Imagine trying to find something that, when multiplied by itself, gives you a negative result. This isn’t possible with ordinary numbers. But in real life — like in science, engineering, or even technology — such problems do appear. So, to make sense of those, mathematicians came up with a smart solution: they invented a new type of number to fill the gap.
These numbers help us solve puzzles that were previously impossible. And that’s where this chapter begins — introducing students to the idea of going beyond the usual and exploring something totally new and powerful.
🔍 What’s Covered in Exercise 1.1?
Exercise 1.1 introduces students to this new concept step-by-step. It explains how these special numbers work, how to recognize their different parts, and how to use them in everyday mathematical problems. Instead of jumping into technical details, think of this exercise as learning a new language — one that will help you solve bigger and more complex problems later on.
Here’s what you’ll understand:
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How these new numbers are written and read
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What makes them different from ordinary numbers
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How to combine them, compare them, and represent them in simple ways
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How to visualize them using a basic graph
All of these ideas are explained using simple examples in the lesson video, and students can also follow along in the textbook.
🔽 Ex 1.1 PDF Solutions:
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🧠 Thinking Differently: Real + Imaginary
One of the most exciting parts of this topic is that it asks students to think in a completely different way. Until now, math has always been about real, countable things — like how many apples, how much distance, or how many hours. But now, you’re introduced to something called the “imaginary” part of numbers.
Don’t be confused by the name — it doesn’t mean it’s not real or useful. It simply means it’s something new and different, made for solving specific kinds of problems. This combination of “real” and “imaginary” parts makes the topic feel almost like a mix of science and art — opening up a new way of thinking.
🎨 Visualizing Ideas with Diagrams
Exercise 1.1 also teaches students how to see these new numbers on a flat surface — like plotting a point on a simple graph. This helps learners connect numbers to pictures, making abstract ideas easier to understand. With just two directions — side to side and up and down — students can now picture where these numbers “live” on a map.
This visual technique becomes even more helpful when students start solving problems, as it shows the full journey of a number — where it starts, where it ends, and how far it has moved.
✍️ Practice Makes Progress
This exercise encourages students to work through various examples to become comfortable with these new types of numbers. Through consistent practice, learners begin to:
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Build confidence in recognizing and working with new number types
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Understand how to read and write answers in standard formats
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Develop a stronger base for future topics
The goal is to remove any fear and confusion, and make this new concept feel just as familiar as the numbers you’ve always used.
Free Resources and Extra Help
To make things even easier for students, we have created step-by-step PDF notes for this exercise. These notes are available for free download on our website and include:
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