What is the Best Book on Complex Numbers for Beginners?

In summary, based on your preferences, the best book on complex numbers for you would be one that covers the basics in great detail and includes high order thinking problem sets for practice. You are aiming to finish the entire course on complex numbers, which is used in electrical engineering. The book with good reviews and at a low cost is available for purchase or can be obtained from the library. The book is "Complex Variables: Introduction and Applications" by Mark J. Ablowitz and A. S. Fokas, available for $7 used on Amazon.
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rohit dutta
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Which is the best book on complex numbers? I'm new to this topic so I would like to begin my study with the basics. I prefer books that deal with concepts in a great detail for a better understanding. The book must also contain good problem sets(high order thinking) for practise. I'm aiming to finish the entire course on complex numbers since it is used in the field of electrical engineering.

Anticipating a reply at the earliest.
 
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1. What are complex numbers?

Complex numbers are numbers that are expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit (√-1). They can be thought of as extensions of the real numbers, where the imaginary unit i represents the square root of -1.

2. How are complex numbers used in science?

Complex numbers are used in various fields of science, including physics, engineering, and mathematics. They are particularly useful in electrical engineering, where they are used to represent and analyze AC circuits. They are also used in quantum mechanics to describe the behavior of particles and in signal processing to analyze and filter signals.

3. What is the significance of the letter "i" in complex numbers?

The letter "i" is used to represent the imaginary unit (√-1) in complex numbers. It is used as a placeholder because there is no real number that can be squared to give a negative result. The use of "i" makes it easier to perform calculations with complex numbers and to understand their properties.

4. How are complex numbers represented graphically?

Complex numbers can be represented graphically on the complex plane, which is a two-dimensional coordinate system where the horizontal axis represents the real part of the complex number and the vertical axis represents the imaginary part. The location of a complex number on the complex plane is known as its coordinates or Cartesian form.

5. What is the conjugate of a complex number?

The conjugate of a complex number a + bi is a - bi. In other words, it is the complex number with the same real part but the opposite imaginary part. The conjugate is important in complex number operations, such as division, and is also used to find the modulus (absolute value) of a complex number.

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