BASIC
TRIG
CST-I
CST-II
Quadr. Eq.
LCM
GCD
zn=c
,
Number Factor.
ex
ln
loga
nCr
Number Divisors
sin
cos
tan
nPr
%
√ x 
x2
xy
x!
n√ x 
π
2π
cot
sec
csc
sin-1
cos-1
tan-1
cot-1
sec-1
csc-1
sinh
cosh
tanh
coth
sech
csch
sinh-1
cosh-1
tanh-1
coth-1
sech-1
csch-1
φ
c
G
h
h
μ0
ε0
Z0
κ
qe
μB
G0
G0-1
f0
μN
RK
Mu
M12C
gn
lP
mP
tP
qP
TP
a0
re
me
GF
α
Eh
mp
md
mn
h/2me
R∞
σt
mu
NA
k
F
c1
n0
R
NA·h
Vm
c2
σ
b
Rec/Pol
r∠θ
i
⌫
AC
C
(
1
2
3
+
)
4
5
6
−
DEG
7
8
9
×
AUTO
0
.
=
/
  
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Complex Number Calculator

This Online Scientific Calculator https://www.nanocalculator.com performs operations on Complex Numbers in cartesian and polar form, solves Quadratic Equations with real and complex coefficients, finds the Least Common Multiple (LCM) and the Greatest Common Divisor (GCD). It also finds the n-th roots of a real or complex number. Many useful built-in basic physical constants. Use complex numbers as if they were real, put them in any function you want in either cartesian or polar form, and mix forms. You can enter the ∠ symbol by typing the capital letter L. The calculator works with your keyboard, mouse or a combination of both.

Unlike the oversimplified examples, you always use parentheses.
That way, if the operations are not performed, it's because you typed:

 

Examples of how to use the Calculator

Here are some examples of how to use the calculator. If you don't use parentheses in the functions, the calculator may not be able to do the calculations.

π
The mathematical constant $π \approx 3.14$
√ x 
9
Square root calculation $\sqrt{9} = 3$
5
x2
Square calculation $5^{2} = 25$
ex
4
Calculate an exponential function $e^{4} = 54.598150033144236$
ln
5
Natural logarithm calculation $\ln(5) = 1.6094379124341003$
5
nCr
3
Calculate combinations $\binom{5}{3}=10$
5
nPr
3
Calculate permutations $P_3^5=60$
3
xy
4
Calculate powers $3^{4} = 81$
sin
9
0
Calculate the sine $\sin(90^{\circ}) = 1$
tan
4
5
Calculate the tangent $\tan(45^{\circ}) = 1$
cos
−
6
0
Calculate the cosine $\cos(-60^{\circ}) = 0.5$
3
0
%
7
Calculate the reminder of the Euclidean division, $30\!\!\mod 7 = 2$
5
+
2
0
%
Operations with percentages $5+20\% = 6$
5
×
2
0
%
Operations with percentages $5\cdot 20\% = 1$
loga
1
0
0
Calculate a decadic logarithm (base 10), $\log_{10}(100) = 2$
loga
(
8
,
2
)
Calculate a binary logarithm (base 2), $\log_{2}(8) = 3$
Number Divisors
5
0
Find the divisors of a natural number 50: 1,2,5,10,25,50
Number Factor.
1
2
6
Prime factorization of natural numbers $126 = 2 \cdot 3^{2}\cdot 7$
n√ x 
(
8
,
3
)
Calculate the cube root $\sqrt[3]{8} = 2$
GCD
2
4
,
3
6
Greatest Common Divisor (GCD) Calculation GCD(24,36)=12
LCM
3
,
4
,
6
Least Common Multiple (LCM) Calculation LCM(3,4,6) = 12
Quadr. Eq.
1
,
−
3
,
2
Solve Quadratic Equations (QE) $x^2-3x+2=0$. Roots $1, 2$.
(
7
−
4
i
)
+
(
−
6
−
9
i
)
Adding complex numbers $7-4i+(-6-9i) = 1 - 13i$
(
−
3
+
5
i
)
−
(
7
+
4
i
)
Subtracting complex numbers $-3+5i-(7+4i) = -10 + i$
(
−
9
−
8
i
)
×
(
4
+
7
i
)
Multiplying complex numbers $(-9-8i)\cdot(4+7i) = 20 - 95i$
(
8
−
2
i
)
/
(
−
5
−
3
i
)
Dividing complex numbers $\frac{8-2i}{-5-3i} = -1 + i$
5
r∠θ
3
0
+
2
r∠θ
4
5
Adding complex numbers in polar form $5 \angle 30^{\circ} + 2 \angle 45^{\circ} = 6.95115 \angle 34.271^{\circ}$
5
r∠θ
3
0
−
2
r∠θ
4
5
Subtracting complex numbers in polar form $5 \angle 30^{\circ} - 2 \angle 45^{\circ} = 3.11151 \angle 20.424^{\circ}$
5
r∠θ
3
0
×
2
r∠θ
4
5
Multiplying complex numbers in polar form $5 \angle 30^{\circ} \cdot 2 \angle 45^{\circ} = 10 \angle 75^{\circ}$
5
r∠θ
3
0
/
2
r∠θ
4
5
Dividing complex numbers in polar form $\frac{5 \angle 30^{\circ}}{2 \angle 45^{\circ}} = 2.5 \angle -15^{\circ}$
6
r∠θ
3
0
Rec/Pol
Converting a complex number from polar to rectangular form $6 \angle 30^{\circ} = 5.19615242+3i$
2
+
2
i
Rec/Pol
Converting a complex number from rectangular to polar form $2+2i = 2.82842712 \angle 45^{\circ}$
zn=c
1
,
6
find all roots of unity of order 6, $z^{6} = 1 \Leftrightarrow (z=1 \lor z=1∠60° \lor z=1∠120° \lor z=-1 \lor z=1∠-120° \lor z=1∠-60°)$
zn=c
−
1
1
9
−
1
2
0
i
,
4
find all roots of a complex number of order 4, $z^4 = -119-120i \Leftrightarrow z \in \{ 3-2i, 2+3i, -3+2i, -2-3i \}$
sin
(
5
r∠θ
3
0
)
+
loga
(
2
r∠θ
4
5
,
1
−
i
)
$\sin(5 \angle 30^{\circ}) + \log_{2 \angle 45^{\circ}}(1-i) = -6.2007288135-1.1487948323i$
Quadr. Eq.
1
,
2
−
2
i
,
−
(
7
+
2
6
i
)
Solving quadratic equations with complex coefficients $z^2+(2-2i)z-(7+26i)=0$. Complex roots $3+4i$, $-5-2i$.

Calculator.gr This calculator is equipped to handle operations involving complex numbers in both Cartesian and polar forms. It has the capability to solve quadratic equations with real and complex coefficients, determine the Least Common Multiple (LCM) and the Greatest Common Divisor (GCD), and find the nth roots of a real or complex number. Additionally, the calculator includes various built-in basic physical constants. Users can employ complex numbers in diverse functions, inputting them in either Cartesian or polar form, and even combining both forms. For user convenience, the calculator is compatible with keyboard, mouse, or a combination of both.

NanoCalculator Complex Number Calculator This calculator can perform operations on complex numbers in both Cartesian and polar forms. It can solve quadratic equations with real and complex coefficients, find the Least Common Multiple (LCM) and the Greatest Common Divisor (GCD), and find the nth roots of a real or complex number. The calculator also has many basic physical constants built in. Users can use complex numbers in various functions, entering them in either Cartesian or polar form and even combining both forms. The calculator is compatible with keyboard, mouse, or a combination of both for ease of use.

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