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Symbolic polar angle




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


Compute Polar Angle of Numeric Inputs

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 Polar Angle of Symbolic Inputs

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 Polar Angle of Symbolic Expressions

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 Polar Angle of Array

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]

Input Arguments

collapse all

Input, specified as a number, vector, matrix, array, or a symbolic number, variable, expression, function.


  • 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.


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

Version History

Introduced in R2013a

See Also

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