Available Functions

Working with Complex Numbers

Complex numbers can be entered in the following formats:

• a+bi: e.g., 3+2i
• a-bi: e.g., 3-2i
• bi: e.g., 2i (for purely imaginary numbers)
• a: e.g., 3 (for real numbers)

Complex Number Operations

• Addition: (a+bi) + (c+di) = (a+c) + (b+d)i
• Subtraction: (a+bi) - (c+di) = (a-c) + (b-d)i
• Multiplication: (a+bi)(c+di) = (ac-bd) + (ad+bc)i
• Division: (a+bi)/(c+di) = ((ac+bd)/(c²+d²)) + ((bc-ad)/(c²+d²))i

Complex Functions

• conj(z): Complex conjugate of z
• |z|: Magnitude (absolute value) of z
• arg(z): Argument (phase) of z in radians
• exp(z): Complex exponential function
• ln(z): Complex natural logarithm

Matrix Calculator

The matrix calculator allows you to perform various operations on matrices:

• Determinant: Calculate the determinant of a square matrix
• Inverse: Find the inverse of a square matrix
• Transpose: Transpose the rows and columns of a matrix
• Rank: Calculate the rank of a matrix
• Eigenvalues: Find the eigenvalues of a square matrix
• Scalar Multiplication: Multiply a matrix by a constant

How to Use

1. Set the number of rows and columns for your matrix
2. Enter values in each cell of the matrix
3. Select the operation you want to perform
4. Click "Calculate" to see the result

Note: Some operations (like inverse and determinant) require a square matrix. The calculator will notify you if your matrix doesn't meet the requirements for the selected operation.

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