Complex numbers are useful in representing a phenomenon that has two parts varying at the same time, for instance an alternating current.

Complex Numbers

**“Imaginary numbers are a ﬁne and wonderful refuge of the divine
spirit almost an amphibian between being and non-being. ”**

**- Gottfried Leibniz**

Many mathematicians contributed to the full development of complex
numbers. The rules for addition, subtraction, multiplication, and division of
complex numbers were developed by the Italian mathematician Rafael Bombelli. He
is generally regarded as the first person to develop an algebra of complex
numbers. In honour of his accomplishments, a moon crater was named Bombelli.

Complex numbers are useful in representing a phenomenon that has
two parts varying at the same time, for instance an alternating current.
Engineers, doctors, scientists, vehicle designers and others who use
electromagnetic signals need to use complex numbers for strong signal to reach
its destination. Complex numbers have essential concrete applications in signal
processing, control theory, electromagnetism, fluid dynamics, quantum
mechanics, cartography, and vibration analysis.

Upon completion of this chapter, students will be able to:

● perform algebraic
operations on complex numbers

● plot the complex
numbers in Argand plane

● find the conjugate and
modulus of a complex number

● find the polar form and
Euler form of a complex number

● apply de Moivre theorem
to find the nth roots of complex numbers.

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12th Mathematics : UNIT 2 : Complex Numbers : Introduction | Complex Numbers

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