ABSTRACT
At the end of this chapter, you should be able to:
• state De Moivre’s theorem • calculate powers of complex numbers • calculate roots of complex numbers • state the exponential form of a complex number • convert Cartesian /polar form into exponential form and vice-versa. • determine loci in the complex plane
From multiplication of complex numbers in polar form,
(r∠θ)× (r∠θ) = r2∠2θ
Similarly, (r∠θ)×(r∠θ)×(r∠θ)=r3∠3θ , and so on. In general, De Moivre’s theorem∗ states:
[r∠θ ]n= rn∠nθ The theorem is true for all positive, negative and fractional values of n. The theorem is used to determine powers and roots of complex numbers.