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Complex number calculator

This calculator finds the square root, modulus, inverse, conjugate and converts complex numbers to polar form. The solver explains each operation in detail, step by step.

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This calculator allows you to input square roots (just type r in front of the number). For example : $ 2.4342 = \text{r(397/67)} = \sqrt{ \frac{ 397 }{ 67 } } . $

Enable "Find approximate solution" option by clicking checkbox at the bottom.

Operations with complex number

modulus, conjugate, root, inverse, polar form
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Enter complex number:

Z = i

To enter square roots, type letter r $ \left( \color{blue}{\text{ r17 } = \sqrt{17}} ~ \right) $. Examples:

z=4+6i

z=2-3/2i

z=√2-√5i

Choose what to compute:

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439 968 265 solved problems

Modulus (Magnitude)	Conjugate
Inverse	Roots
Polar form

ID	Problem	Count
1	Find the modulus of $$ z = 6+3i $$	162
2	Find the modulus of $$ z = 2+i $$	151
3	Find the inverse of $$z = 4+3i$$	133
4	Find the modulus of $$ z = 0 $$	88
5	Find the modulus of $$ z = -2+4i $$	40
6		38
7	Find the modulus of $$ z = 2+3i $$	31
8	Find the modulus of $$ z = -1+\sqrt{ 3 }i $$	31
9	Find the modulus of $$ z = 1+\sqrt{ 3 }i $$	27
10	Find the modulus of $$ z = -i $$	25
11	Find the modulus of $$ z = -3i $$	23
12	Find the modulus of $$ z = 2+2i $$	22
13	Find the modulus of $$ z = 1+i $$	22
14	Find the modulus of $$ z = 5-5i $$	22
15	Find the modulus of $$ z = 1-\sqrt{ 3 }i $$	22
16	Find the modulus of $$ z = \sqrt{ 3 }-i $$	22
17	Find the modulus of $$ z = 8-3i $$	21
18	Find the modulus of $$ z = \sqrt{ 2 }-\sqrt{ 2 }i $$	21
19	Find the modulus of $$ z = 1+i $$	20
20	Find the modulus of $$ z = 4+6i $$	20
21	Find the modulus of $$ z = -1+i $$	19
22	Find the modulus of $$ z = 3 \sqrt{ 3 }-3i $$	18
23	Find the modulus of $$ z = - \frac{\sqrt{ 2 }}{ 2 }- \frac{\sqrt{ 2 }}{ 2 }i $$	18
24	Find the inverse of $$z = 1+\sqrt{ 3 }i$$	18
25	Find the modulus of $$ z = 3-4i $$	18
26	Find the modulus of $$ z = 3+4i $$	17
27	Find the modulus of $$ z = -3+3 \sqrt{ 3 }i $$	17
28	Find the modulus of $$ z = \frac{ 3 \sqrt{ 3}}{ 2 }+\frac{ 3 }{ 2 }i $$	17
29	Find the modulus of $$ z = 3+4i $$	17
30	Find the modulus of $$ z = \sqrt{ 3 }+i $$	17
31	Find the modulus of $$ z = 7-3i $$	17
32	Find the modulus of $$ z = -4i $$	16
33	Find the modulus of $$ z = \frac{ 1 }{ 2 }+\frac{ 3 }{ 4 }i $$	15
34	Find the modulus of $$ z = 3-4i $$	15
35	Find the modulus of $$ z = 1 $$	15
36	Find the modulus of $$ z = -2-2i $$	15
37	Find the modulus of $$ z = -5-5i $$	15
38	Find the modulus of $$ z = -i $$	15
39	Find the modulus of $$ z = 6-3i $$	14
40	Find the modulus of $$ z = 2-4i $$	14
41	Find the roots of $$z = 1+\sqrt{ 3 }i$$	14
42	Find the modulus of $$ z = 3-i $$	14
43	Find the modulus of $$ z = -5+3i $$	14
44	Find the modulus of $$ z = -2 $$	14
45	Find the modulus of $$ z = -2 $$	14
46	Find the modulus of $$ z = -1+\sqrt{ 3 }i $$	14
47	Find the modulus of $$ z = -1-\sqrt{ 3 }i $$	14
48	Find the modulus of $$ z = -3 $$	13
49	Find the modulus of $$ z = 5-2i $$	13
50	Find the modulus of $$ z = 1-i $$	13

Complex number calculator

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Complex modulus, roots, inverse – Solved Problems Database