🔢 Complex Numbers Operations
Enter one or two complex numbers and select an operation to calculate the result.
Enter the numbers and select an operation to see the result.
📘 Operations on Complex Numbers
Complex numbers are in the form \(a + bi\), where \(a\) is the real part and \(b\) is the imaginary part. The operations are:
Unary Operations
- Inverse: \( \frac{1}{a + bi} \)
- Conjugate: \( a - bi \)
- Modulus: \( |a + bi| = \sqrt{a^2 + b^2} \)
- Polar Form: \( r \angle \theta \), where \( r = \sqrt{a^2 + b^2} \) and \( \theta = \tan^{-1}\left(\frac{b}{a}\right) \)
- Logarithm: \( \log(a + bi) \)
- Exponential: \( e^{a+bi} \)
- Sine, Cosine, Tangent: Trigonometric forms of complex numbers.
Binary Operations
- Addition: \( (a + bi) + (c + di) = (a + c) + (b + d)i \)
- Subtraction: \( (a + bi) - (c + di) = (a - c) + (b - d)i \)
- Multiplication: \( (a + bi) \cdot (c + di) = (ac - bd) + (ad + bc)i \)
- Division: \( \frac{(a + bi)}{(c + di)} \)
- Power: \( (a + bi)^n \)
