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TRIGONOMETRY AND THE COMPLEX PLANE
In previous units, complex
numbers were introduced and explored, and the “ArcTangent”
was used to find to rotation angles when two complex numbers were multiplied.
The complex plane and trigonometry are intricately related and have many
applications in modern technology. Computer circuitry and electronics are
highly dependent on the interconnections between trigonometry and complex
numbers. In the branch of mathematics known as “Analytic Number Theory”,
complex numbers, trigonometry, and logarithms may hold the key to
discerning a pattern for the distribution of prime numbers. Since high-level
security systems depend on the prime factors of composite integers, a method
for deciding the distribution of prime numbers would be an invaluable tool for
government and private use. In this unit we will explore the relationships
between trigonometry and complex numbers, develop methods for converting
complex numbers to trigonometric form (and vice versa), and we will find roots
of complex numbers using trigonometric techniques.
