## IBDP Mathematics Applications & Interpretations HL Chapter 5 Notes

complex numbers

STUDY NOTES FOR MATHEMATICS – CHAPTER 5 – COMPLEX NUMBERS

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All DP mathematics courses serve to accommodate the diverse range of needs, interests and abilities of students, and to fulfill the requirements of various university and career aspirations. The aims of these courses are to enable students to: develop mathematical knowledge, concepts, principles, logical, critical and creative thinking, employ and refine their powers of abstraction and generalization. Students are also encouraged to appreciate the international dimensions of mathematics and the multiplicity of its cultural and historical perspectives.

Complex numbers can be written in Cartesian forms. These complex numbers can be represented on a complex plane also known as an Argand plane where the x axis is the real axis and the y axis is the imaginary axis. Since these complex numbers are represented through vectors on the Argand plane, they have a magnitude and a direction, which are modulus and argument respectively. The modulus is a+bi and the argument is the square root of the addition of the squares of the variables in the cartesian form. They can alternatively be written in a polar form also known as the modulus-argument form. Additionally, the concept of geometry and transformation in a complex plane will also be covered. There is also a third way to write the complex number, which is known as the Euler’s form which is Euler’s formula insert. In case of unknown powers in the polar form of the complex number, a theorem namely De Moivre’s Theorem can be performed which is the de moivre theorem equation insert. Using this theorem, the roots of the complex numbers can be found. The nth roots of a complex number c are the n solutions of z^n=c. 