ALG-25

Complex modulus

Polar radius.

Reading speed

Algebracomplex

Governing equation

|z|=\\sqrt{x^2+y^2}

where

x: x (—)
y: y (—)
|z|: |z| (—)

Lecture brief

Historical brief

From al-Khwārizmī’s restoration to the quadratic formula, AM–GM, De Moivre and logarithms, algebra is the closed-form skeleton under every lab. These sheets solve, bound and compound. This sheet (ALG-25 — Complex modulus) is the form associated with complex. Working symbols: $x$ , $y$ $\rightarrow$ $|z|$ . Polar radius.

Purpose

Purpose: compute

|z|

from

x

y

in Algebra via

|z|=\\sqrt{x^2+y^2}

Polar radius. Use it when a real algebra question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

x = 3.000\,\mathrm{—}

y = 4.000\,\mathrm{—}

, the governing relation

|z|=\\sqrt{x^2+y^2}

yields

|z| = 5.000\,\mathrm{—}

. Polar radius. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

x x3 —y y4 —

Outputs

|z| |z|5.000 —

Reading speed

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Narration of this film

Polar radius.

Reading speed

Watch on YouTube