Used in entering a vector in polar, cylindrical, or spherical format, or a complex number in polar form.

[*r*,∠*θ*]

[*r*,∠*θ*,*z*]

[*r*,∠*θ*,∠*φ*]

(*r*∠*θ*)

**Menu Location**

- Press 2nd MATH to enter the MATH menu.
- Press 2 to enter the Angle submenu.
- Press 7 to select ∠.

This command works on all calculators.

1 byte

The ∠ operator is used for alternate forms of entering vectors or complex numbers. It will be used for output depending on the Complex Format and Vector Format mode settings, but you can always use it in an expression.

For vectors (which are just 1x2 or 1x3 matrices, as far as ∠ is concerned):

- [r,∠θ] is equivalent to [r*cos(θ),r*sin(θ)]
- [r,∠θ,z] is equivalent to [r*cos(θ),r*sin(θ),z]
- [r,∠θ,∠φ] is equivalent to [r*cos(θ)*sin(φ),r*sin(θ)*sin(φ),r*cos(φ)]

These have to be row vectors — you can't use column vectors with ∠.

For complex numbers, (r∠θ) is equivalent to r*(cos(θ)+* i**sin(θ)). You have to have the parentheses there, and both r and θ must be real numbers or expressions.

# Error Conditions

**260 - Domain error** happens when complex numbers are used in the vector notation.

**580 - Invalid polar complex** happens when the values of r and θ in the complex number notation are invalid.

**640 - Invalid vector syntax** happens when the ∠ mark is misplaced in the vector notation.