Complex Numbers in Spreadsheets: Rectangular & Polar Form, Arithmetic, Powers & Roots, Rotations and AC Phasors
Make complex numbers concrete with two columns. You will add, multiply and divide numbers written as real and imaginary parts, convert to modulus and angle, multiply in polar form, raise to powers and take roots with De Moivre, rotate shapes in the plane and solve simple AC circuits with phasors, with every cell checked as you go.
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About this course
This course keeps every complex number in two spreadsheet columns, one for the real part and one for the imaginary part, so each step is a formula you can read. You plot numbers on the complex plane, write conjugates and multiply out products and quotients by hand. You compute modulus and argument with SQRT and ATAN plus a quadrant correction, switch between rectangular and polar form, and raise numbers to powers and take n-th roots with De Moivre's rule. Then you rotate and scale a shape by one multiplication, solve quadratic equations with complex roots and check them by substitution, and finish with impedances, phase angles and currents in fictional AC circuits.
Lessons
- The Complex Plane: Real & Imaginary Columns, Quadrants and Conjugates Pro
- Complex Arithmetic: Sums, Products (ac − bd, ad + bc) and Division by the Conjugate Pro
- Modulus & Argument: Distances, ATAN with a Quadrant Correction, Degrees vs Radians Pro
- Polar Form: r(cos θ + i sin θ), Multiplying Moduli and Adding Angles Pro
- Powers & Roots: De Moivre's Rule, n-th Roots and the Roots of Unity Pro
- Rotations & Scaling: Multiplying a Shape by a Complex Number Pro
- Quadratic Equations: Negative Discriminants, Complex Root Pairs and Checking by Substitution Pro
- AC Phasors: Impedance R + jX in Series and Parallel, Current Magnitude and Phase Angle Pro