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Symbolic polar angle




angle(Z) computes the polar angle of the complex value Z.

Input Arguments


Symbolic number, variable, expression, function. The function also accepts a vector or matrix of symbolic numbers, variables, expressions, functions.


Compute the polar angles of these complex numbers. Because these numbers are not symbolic objects, you get floating-point results.

[angle(1 + i), angle(4 + pi*i), angle(Inf + Inf*i)]
ans =
    0.7854    0.6658    0.7854

Compute the polar angles of these complex numbers which are converted to symbolic objects:

[angle(sym(1) + i), angle(sym(4) + sym(pi)*i), angle(Inf + sym(Inf)*i)]
ans =
[ pi/4, atan(pi/4), pi/4]

Compute the limits of these symbolic expressions:

syms x
limit(angle(x + x^2*i/(1 + x)), x, -Inf)
limit(angle(x + x^2*i/(1 + x)), x, Inf)
ans =
ans =

Compute the polar angles of the elements of matrix Z:

Z = sym([sqrt(3) + 3*i, 3 + sqrt(3)*i; 1 + i, i]);
ans =
[ pi/3, pi/6]
[ pi/4, pi/2]


For real X and Y such that Z = X + Y*i, the call angle(Z) is equivalent to atan2(Y,X).

More About

collapse all


  • Calling angle for numbers (or vectors or matrices of numbers) that are not symbolic objects invokes the MATLAB® angle function.

  • If Z = 0, then angle(Z) returns 0.

See Also

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Introduced in R2013a

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