Euler’s Formula

AC Circuits: I-V Relationships, Impedance, Admittance, and Power

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Menu (linked Index) AC Circuit Basics: i-v Relationships, Impedance, Admittance, and Power Last Update: January 14, 2026 Introduction Pure Resistor AC Circuit Pure Inductor AC Circuit Pure Capacitor AC Circuit Pure Inductor and Capacitor Impedance – Frequency Domain Analysis Summary: Pure Element AC Circuits Phasor Basics Series RLC AC Circuits (Voltage → Impedance → Power […]

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Sine and Cosine – Definitions and Properties

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Menu (linked Index) Sine and Cosine – Definitions and Properties Last Update: December 23, 2025  Introduction History Etymology Unit Circle Trigonometry Sine and Cosine Wave From the Unit Circle Sinusoid Waveform General Characteristics Circular Motion Parameters Phase Angle Expression Using Rotational Kinematics General Equations for Instantaneous AC Voltage and Current Voltage and Current Waveform Characteristics

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Circuit Analysis Math Basics: Trig, Complex Numbers, and Euler’s Equation

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Menu (linked Index) Circuit Analysis Math Basics: Trig, Complex Numbers, and Euler’s Equation Last Update: November 19, 2025 Introduction Right Triangle Trigonometry Unit Circle Complex Numbers Powers of the Imaginary Unit j Multiplier Rotates Z Cosine and Sine Expressions Using Euler’s Equation ejθ spins ejwt spins Introduction This article explores the basic math that underpins

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Euler’s Formula Derivation

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Menu (linked Index) Euler’s Formula Derivation Last Update: December 12, 2024  Introduction The Derivative Derivative Rules Derivatives of Useful Functions Taylor and Maclaurin Power Series Euler Formula Derivation  Summary of the Derivation Conclusion Appendix 1 – Graphical meaning of (x-a) Appendix 2 – Full Derivation of Taylor and Maclaurin Power Series  Appendix 3 – Unit

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Complex Number z = a + bi icon

Complex Numbers

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Menu (linked Index) Complex Numbers Last Update: November 29, 2024 Introduction Multiplying by -1 The Imaginary Unit i Multiplying by i  Complex Numbers and Complex Plane Multiplying by i in the Complex Plane Polar / Trigonometric Form of a Complex Number Polar / Exponential Form of a Complex Number Euler’s Formula is All about Rotation

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