Complex Numbers in Spreadsheets: Rectangular & Polar Form, Arithmetic, Powers & Roots, Rotations and AC Phasors

What you'll build

What you will be able to do

Each lab ends with a concrete result that you build yourself and the checker confirms, cell by cell.

• Store six complex numbers as real and imaginary columns, write their conjugates, show that z · z̄ is always a real number, name the quadrant of each point and count the numbers above the real axis.
• Add, multiply and divide four pairs of complex numbers part by part, so every result is again a real column and an imaginary column.
• Compute the modulus of seven numbers with SQRT, see where plain ATAN goes wrong, build an argument formula that is right in all four quadrants and on the axes, and convert it to radians.
• Turn two numbers given as modulus and angle into rectangular parts, multiply them with the polar rule, and confirm that the rectangular rule from lesson 2 gives the same product.
• Raise z = 1.1∠50° to the powers 1 to 8 with De Moivre's rule and find all four fourth roots of w = 16∠120°, spaced evenly around a circle.
• Build the multiplier m = 1.5∠30°, apply it to every corner of a house-shaped logo, and draw the turned and enlarged outline as a scatter chart.
• Classify six quadratic equations by their discriminant, compute the centre and spread of their roots, and prove one complex root correct by putting it back into the equation.
• Treat impedances as complex numbers: the size and phase angle of five series circuits, their currents, and the combined impedance of two branches in parallel.