SU61127A1 - A device for multiplying and dividing complex numbers - Google Patents

Description

Instruments for multiplying and dividing complex numbers, consisting of a rotary disk with two families of curves plotted for the logarithms of the modules, are already known.

In the proposed instrument, circumferential divisions are applied to the circumference of the disk, which are used for counting the argument using a ruler around the disk center of the Linea with two movable sliders in each other, equipped with transverse risks, combined with the real and imaginary parts of the complex numbers.

The turning disk and turning ruler are installed on a common axis, strengthened in the center of the main board of the device.

FIG. 1 shows the proposed device, a top view with a rotating ruler mounted on it; in fig. 2 is a cross section of a ruler and in FIG. 3 - shchala, deposited on the rotary disk of the device.

The device consists of a main board /, in the center of which the axis is fixed //. This axis is worn and can be rotated through a 360 ° disc /// and Ruler IV. The disk /// contains a diagram of two intersecting families of curves, and the IV line has two sliders of transparent celluloid, one long and the second short. The cross section of the ruler is shown in FIG. 2, from which it can be seen that the second slider is inside the first one and can move with it without changing their relative position.

The rotation of the disk and the rulers are independent, i.e. when the disk is rotated, the ruler is stationary and vice versa.

The following are plotted on the disk: a system of curves having the equation G L + B Ig t-- and the corresponding positive and negative values of the real part of the complexes in polar coordinates, and the second system of curves with the equation Г2 Л + В / g -: - corresponding to the imaginary part of the complex. The value of K is set on the curves. The coefficients A and B for all curves are the same.

On the x-axis of the scale, the symbols +1, -1, + / and - / are put.

On a stationary board / labeled O for setting the disk to the zero position. On a large engine, one longitudinal risk coincides with the radius and two transverse risks with a distance between them corresponding to a change in the K value ten times. On the small engine there is only one transverse risk.

The diagram also contains the initial circle, passing through the K 1 values on all four axes.

The internal risk of a large engine is indicated by the letter a, the second risk is the letter b, and the risk of the small engine is indicated by the letter c. Due to the small scale of the drawing (Fig. 1), the risks of a, b, and c are not inflicted on it and only places for them are marked.

The use of the instrument is as follows:

1. Multiplication of the complex. The disk is set to the initial position, and the risk and combined with the initial circle. By turning the ruler and moving one small engine, it is possible to match the risks with the dot of the diagram corresponding to the complex of one of the factors. Turning the disk to match its axis -1-1 with the longitudinal engine, rotate the ruler again and move the large engine until the risks a or b coincide with the point of the second factor. Having returned the disk to the initial position, one obtains against the risks with the desired value of the complexes of the product. The number of characters is counted as in a conventional counting bar.

2. Division of complexes. Placing the disc in the initial position, combine the risk of a or b with the point of the complex of the dividend. Turning the disk and moving the small engine, combine the risk with the dot of the complex divider. Rotate the ruler to align with the axis of the +1 disk and shift the large slider to align the risks with the initial circle. By returning the disk to the initial position, the desired value of the private complex is obtained against the risks L.

3. Finding the inverse collex (i.e. division of the unit by the complex). Having established the risk a on the initial circle, combine the risk with the given complex. By moving the big slider before combining the risks with the initial circle, the value of the complex associated with the desired is obtained against the risks L. After that, it remains only to change his sign in front of the imaginary part and the reverse.

4. The finding of the complex modulo and argument. Aligning the ruler with the axis f 1, set any of the tick marks to the value of / C corresponding to the given module. Turning the ruler to the angle of a given argument, against the same risks get the desired complex.

5. The definition of the module and the argument on the complex is made back to the previous case.

To construct a diagram, you can use the property of curves not to change the distance in the direction of the radius. This makes it possible to make one exact pattern and apply all the curves on it. The line with the drawing device should slide one end along the template and the other along the axis. By changing the position of the drawing device, all curves of one half of the disk are obtained. Turning the disk 90, 180 and 270 °, get the rest of the curves.

It is more convenient to make these curves by engraving on metal, and then transfer to disk. Subject invention

A device for multiplying and dividing complex numbers, consisting of a rotary disk with two families of curves applied to it for logarithms of modules, characterized by the use of a ruler rotatable around the disk center with two movable sliders in each other, equipped with real and imaginary parts. complex numbers.

L 61127

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