7.5-04 Growth and turning

Growth and turning

Interpret the modulus and argument of a conjugate eigenpair in discrete evolution. Follow repeated scaling and turning, check quadrants and distinguish bounded motion from convergence and periodicity.

What you will practise

• Compute modulus and argument
• Accumulate scales and angles
• Classify inward and outward evolution
• Treat unit-modulus motion carefully

Prerequisites and study approach

This microlearning belongs to Module 7, Eigenvalues and Dynamical Systems, in the Complete Linear Algebra Course. Before starting, review complex numbers, rotation blocks and matrix iteration. The questions move from recognition and short calculations to connected reasoning. Single-select questions require one answer; multiselect questions ask you to evaluate every statement independently.

Later questions test the difference between decay of modes and behavior of Euclidean norm in a general basis. Work out your own result before checking the choices, then use the explanation to compare the reasoning and diagnose a mistaken assumption. This focused practice connects conceptual understanding with reliable problem solving and supports review before the next microlearning.