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PHASE function


PHASE(A) returns the phase angle (or angular component) of the complex number A, expressed in radians. This is Excel's IMARGUMENT function.

The argument A can be a real number, a complex number or a matrix. When it is a matrix, the function returns a matrix with the same dimensions and with the PHASE function applied to all elements.

$$ phase(a+bi) = asin\left(b / abs(a+bi) \right) $$

Visual representation

Phase of a complex number


PHASE(2+3i) returns 0.982793723

PHASE(pi()*1i) returns 1.570796327

PHASE(3) returns 0.



See also

Recommended book

Book cover

Complex Numbers from A to ... Z
Titu Andreescu

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Learn how complex numbers may be used to solve algebraic equations, as well as their geometric interpretation Theoretical aspects are augmented with rich exercises and problems at various levels of difficulty