## ABSTRACT

The form used for the Fourier series considered previously consisted of cosine and sine terms. However, there is another form that is commonly used – one that directly gives the amplitude terms in the frequency spectrum and relates to phasor notation. This form involves the use of complex numbers (see Chapter 69). It is called the exponential or complex form of a Fourier series. https://www.w3.org/1998/Math/MathML"> e jθ = cos θ + j sin θ and e − jθ = cos θ − j sin θ https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9780429294402/7a019bd2-8e3e-42f5-a1b0-42593cc08f27/content/eq6065.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> () https://www.w3.org/1998/Math/MathML"> e jθ + e − jθ = 2 cos θ from which, cos θ = e jθ + e − jθ 2 https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9780429294402/7a019bd2-8e3e-42f5-a1b0-42593cc08f27/content/eq6066.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> () https://www.w3.org/1998/Math/MathML"> e jθ − e − jθ = 2 j sin θ from which, sin θ = e jθ − e − jθ 2 j https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9780429294402/7a019bd2-8e3e-42f5-a1b0-42593cc08f27/content/eq6067.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>