In chemistry, the dot square operations of vectors are often needed to calculate the absolute value (modulus) of a vector and modulus square, for example, calculating the kinetic energy of a particle from its velocity. The "||" sign has been commonly adapted in chemistry textbooks for modulus, which is also used in this report. A few typical operations are listed in Fig. . Simple square of a summation (Fig. ) and modulus square calculation (Fig. ) can be combined to obtain vector summation operations of the same particle (Fig. ) and different particles (Fig. ). The vectors of the same particle add up sometimes to form a new vector and then the modulus square of the resulting vector is needed (Fig. ). While the modulus squares of different particles add up independently (Fig. ). These calculations are commonly carried out in many chemistry calculations such as molecular dynamics and quantum chemistry. Two-dimensional (2D) calculations are shown in Fig. while the same rule can be extended to 3D cases. Fig. is a made-up calculation that does not fit well with the same system. The value a is a modulus instead of a unit vector of a defined axis. But because calculating the unit vector length of a given vector is a common need in calculations, it is also added here. Usually in chemistry, this calculation is achieved with the help of an imaginary space that is perpendicular to the real axes. Modulus square calculations for 1D complex values are shown in Fig. . Because a 1D complex number has both real and imaginary parts, "," is used to split the two parts, and ";" is still used to split dimensions. The simple square of a complex number (Fig. ) is usually not interesting in chemistry. Dot operations (Fig. ) are usually more interested in pulling out the modulus square of a complex number. These notations can be extended to calculate the modulus square of the summation of two complex values for the same particle (Fig. ) and two different particles (Fig. ). Fig. only shows 1D complex calculation, notations for 2D and 3D complex calculations can be extended, for example, using (a, ib; c, id; e, if) for a 3D complex number. In summary, a set of notations adapted from computer coding languages and some textbooks are reintroduced to chemistry students. Regardless of whether they have had experience in vector or/and matrix calculations, this set of notations can readily fit in for them to recall and use for vector and complex calculations. It should be easier than the traditional vector and matrix notations because every variable in this system is a unitless and dimensionless numeric value thus intuitive to connect the values to 1D, 2D, 3D, or above calculations. The traditional notations are certainly more efficient to indicate large calculations, but typically simple calculations are taught in chemistry classes making these simple low efficient yet intuitive notations appealing to chemistry students.