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Operations with one complex number

This calculator extracts the square root, calculate the modulus, finds inverse, finds conjugate and transform complex number to polar form. The calculator will generate a step by step explanation for each operation.

Operations with one complex number
Five operations with a single complex number. ( show help ↓↓ )
conjugate (default) modulus
inverse roots
polar form
Use decimals instead of fractions
Hide steps
example 1:ex 1:
Find the complex conjugate of $z = \frac{2}{3} - 3i$.
example 2:ex 2:
Find the modulus of $z = \frac{1}{2} + \frac{3}{4}i$.
example 3:ex 3:
Find the inverse of complex number $3 - 3i$.
example 4:ex 4:
Find the polar form of complex number $z = \frac{1}{2} + 4i$.

Formulas for conjugate, modulus, inverse, polar form and roots


The conjugate of the complex number z = a + bi is: complex conjugate

Example 1: conjugate example 1

Example 2: conjugate example 2

Example 3: conjugate example 3

Modulus (absolute value)

The absolute value of the complex number z = a + bi is: complex modulus

Example 1: modulus example 1

Example 2: modulus example 2

Example 3: modulus example 3


The inverse of the complex number z = a + bi is:

complex inverse

Example 1:

inverse example

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