How To Find The Absolute Value Of A Number

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Circuitous Number Modulus/Magnitude

Tool for calculating the value of the modulus/magnitude of a complex number |z| (absolute value): the length of the segment between the bespeak of origin of the complex plane and the point z

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Complex Number Modulus/Magnitude - dCode

Tag(southward) : Arithmetics, Geometry

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Complex Number Modulus/Magnitude

Mathematics
Arithmetics
Complex Number Modulus/Magnitude

Modulus (Absolute Value) Calculator

Circuitous from Modulus and Argument Reckoner

Answers to Questions (FAQ)

What is the modulus of a complex number? (Definition)

The modulus (or magnitude) is the length (absolute value) in the circuitous plane, qualifying the complex number $ z = a + ib $ (with $ a $ the existent role and $ b $ the imaginary role), information technology is denoted $ | z | $ and is equal to $ | z | = \sqrt{a ^ two + b ^ 2} $.

The module can exist interpreted as the distance separating the signal (representing the complex number) from the origin of the reference of the complex plane.

How to calculate the modulus of a complex number?

To find the module of a complex number $ z = a + ib $ comport out the ciphering $ |z| = \sqrt {a^ii + b^two} $

Instance: $ z = i+2i $ (of abscissa i and of ordinate 2 on the complex plane) so the modulus equals $ |z| = \sqrt{i^2+ii^2} = \sqrt{5} $

How to calculate the modulus of a real number?

The modulus (or magnitude) of a real number is equivalent to its absolute value.

Example: $ |-iii| = three $

What are the backdrop of modulus?

For the complex numbers $ z, z_1, z_2 $ the complex modulus has the following properties:

$$ |z_1 \cdot z_2| = |z_1| \cdot |z_2| $$

$$ \left| \frac{z_1}{z_2} \right| = \frac{|z_1|}{|z_2|} \quad z_2 \ne 0 $$

$$ |z_1+z_2| \le |z_1|+|z_2| $$

A modulus is an absolute value, therefore necessarily positive (or zero):

$$ |z| \ge 0 $$

The modulus of a circuitous number and its conjugate are equal:

$$ |\overline z|=|z| $$

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