Understanding the IMTAN Formula

The IMTAN function in Excel calculates the tangent of a complex number. It's an advanced mathematical tool for complex analysis—like computing tangent values in signal processing, electromagnetic theory, or quantum physics where complex arguments are involved.

IMTAN("3+4i") returns a complex number representing the tangent of 3+4i. It takes an inumber argument (as text in the form "x+yi" or "x+yj"), applying the complex tangent formula tan(x+yi) = [sin(2x) + i⋅sinh(2y)]/[cos(2x) + cosh(2y)]—essential for technical or scientific applications requiring complex trigonometry.

Why Use IMTAN?

IMTAN enables complex trigonometry—think wave mechanics or electrical engineering. Its ability to handle complex arguments extends tangent functionality beyond real numbers, making it valuable for technical disciplines that require complex-domain trigonometric operations.

Example with Sample Data

IMTAN calculates complex tangents: for "3+4i" it returns a complex result with both real and imaginary parts. For a purely real input like "1", it gives the standard tangent value. It's a complex trigonometry calculator.