Mathematics · Complex and Fourier
Complex Modulus Squared Calculator
Calculate modulus squared from real component and imaginary component.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Use c=a²+b² with real component=-5 and imaginary component=12.
- modulus squared=169.
Understand Complex Modulus Squared
One idea, three depths
Choose how deeply to explain Complex Modulus Squared
Complex Modulus Squared: Calculate modulus squared from real component and imaginary component.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Complex Modulus Squared to answer this question: calculate modulus squared from real component and imaginary component? Enter real component and imaginary component; the calculator shows modulus squared. For example: real component=-5 and imaginary component=12 produce modulus squared=169. The answer tells you modulus squared.
Age 15Explain it to a 15-year-oldConnect it to the formula
A complex number's squared modulus is the sum of the squares of its real and imaginary components. This page evaluates the relationship directly. The rule is c=a²+b². Its input values are real component, imaginary component, and the main result is modulus squared. For example: real component=-5 and imaginary component=12 produce modulus squared=169.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated complex modulus squared relation over the valid real-number domain stated below. The implemented relation is c=a²+b², evaluated from real component, imaginary component to produce modulus squared. A complex number's squared modulus is the sum of the squares of its real and imaginary components. This page evaluates the relationship directly. The result loses phase and component signs.
Inputs and valid domain
- real component must be a finite real number.
- imaginary component must be a finite real number.
Important boundary: The result loses phase and component signs.
The formula
c=a²+b²
How the calculator works through it
It substitutes real component, imaginary component into the formula and exposes every numerical step above. The main output is modulus squared.
Read the result correctly
The modulus squared is the direct answer to “calculate modulus squared from real component and imaginary component.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
real component=-5 and imaginary component=12 produce modulus squared=169.
Where this model stops being reliable
The result loses phase and component signs.
Learn it by changing one value
Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.
Dictionary terms behind this calculator
Before studying the codeWhat you should know firstUse the calculator immediately, or check the foundations before reading the implementation.
These foundations help you understand why Complex Modulus Squared works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Complex Modulus Squared uses c=a²+b². You need to recognise what each side represents before substituting the stated inputs or rearranging the relationship.
Review this foundation about 4 min
Strong support
- Complex numbers and components
Real and imaginary components provide the notation needed to interpret Complex Modulus Squared correctly.
Review this foundation about 7 min
Optional enrichment
- Functions and periodic behaviour
A function viewpoint connects Complex Modulus Squared to signals, periodicity and transformations.
Review this foundation about 6 min
Mathematics → algorithm → program
Implement this calculation in code
These are direct reference implementations of the calculator's principal relationship and first output. They run locally and include a small known-answer check where the language supports it.
Algorithm
- Read real component, imaginary component.
- Evaluate the principal relationship: c=a²+b².
- Return modulus squared and check the domain conditions described above.
Python
from math import *
def complex_modulus_squared_calculator(a, b) -> float:
return ((a * a) + (b * b))
assert abs(complex_modulus_squared_calculator(-5, 12) - 169) < 1e-6 * max(1.0, abs(169))
C
#include <assert.h>
#include <math.h>
double complex_modulus_squared_calculator(double a, double b) {
return ((a * a) + (b * b));
}
int main(void) {
const double expected = 169;
const double actual = complex_modulus_squared_calculator(-5, 12);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double complex_modulus_squared_calculator(double a, double b) {
return ((a * a) + (b * b));
}
int main() {
constexpr double expected = 169;
const double actual = complex_modulus_squared_calculator(-5, 12);
assert(std::fabs(actual - expected) < 1e-6 * std::fmax(1.0, std::fabs(expected)));
}
Linux x86-64 assembly
x86-64 NASM · System V ABI · Linux · SSE2 with libm where required
; double complex_modulus_squared_calculator(double a, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global complex_modulus_squared_calculator
section .text
complex_modulus_squared_calculator:
push rbp
mov rbp, rsp
sub rsp, 48
movsd [rbp-8], xmm0
movsd [rbp-16], xmm1
movsd xmm0, [rbp-8]
mulsd xmm0, [rbp-8]
movsd [rbp-32], xmm0
movsd xmm0, [rbp-16]
mulsd xmm0, [rbp-16]
movsd [rbp-40], xmm0
movsd xmm0, [rbp-32]
addsd xmm0, [rbp-40]
movsd [rbp-24], xmm0
movsd xmm0, [rbp-24]
leave
ret
MATLAB
function result = complex_modulus_squared_calculator(a, b)
result = ((a * a) + (b * b));
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[a_, b_] := ((a * a) + (b * b));
Continue in mathematical software
The downloaded file includes your current inputs and first calculated result. It is created locally.
Floating-point answers can differ slightly by language, compiler and processor. Compare within a suitable tolerance rather than assuming every decimal representation will be identical.
Reuse the page responsiblyCite this pageAPA, MLA, Chicago, Harvard, BibTeX and RIS
These formats cite this calculator page itself. They are separate from the academic references above, which support the mathematical method and terminology.
APA 7
MW SysArc. (2026, July 21). Complex Modulus Squared Calculator. MW SysArc Tools. https://math.mwsysarc.com/complex-fourier/complex-modulus-squared-calculator
MLA 9
MW SysArc. “Complex Modulus Squared Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/complex-fourier/complex-modulus-squared-calculator. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Complex Modulus Squared Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/complex-fourier/complex-modulus-squared-calculator.
Harvard
MW SysArc (2026) ‘Complex Modulus Squared Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/complex-fourier/complex-modulus-squared-calculator (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_complex_modulus_squared_calculator_2026,
author = {{MW SysArc}},
title = {Complex Modulus Squared Calculator},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/complex-fourier/complex-modulus-squared-calculator},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Complex Modulus Squared Calculator
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/complex-fourier/complex-modulus-squared-calculator
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Complex Modulus Squared do?
Calculate modulus squared from real component and imaginary component.
How does the Complex Modulus Squared work?
The calculator applies c=a²+b². A complex number's squared modulus is the sum of the squares of its real and imaginary components. This page evaluates the relationship directly.
What can I learn from the Complex Modulus Squared?
It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.
Does MW SysArc receive or store what I enter?
No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.
How should I use the result?
Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.
Last reviewed . Calculations tested .