(45) Complex Number Arithmetic

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Numerical calculations with complex numbers are often tedious and time consuming. It is a pleasure to discover that the computing operations of a recently introduced pocket calculator, the Hewlett-Packard Model 45, enable both the addition (subtraction), and the multiplication (division) of complex numbers to be carried out in an efficient manner. The method for addition, described in the HP-45 Owner's Handbook for vectors, makes use of the ∑+ (∑-) key, which sums (subtracts) in two storage registers (R7 and R8) number pairs previously entered in the X and Y registers. A chain of complex numbers can be multiplied and divided by using the same ∑ key to accumulate the number pairs of the logarithms of each complex factor or divisor. To obtain ln(x+iy) = ln(Re^iθ) from the number pair (x, y) entered in the X and Y registers, press the →P key followed by the ln key. These two operations replace (x, y) by the number pair (lnR, θ), ready to be summed by the ∑+ key for multiplication, the ∑- key for division. After completing these operations for each factor, a press of the recall key followed by the ∑+ key places (∑lnRi, ∑θ) in the X and Y registers. The result is quickly changed to Cartesian form by pressing the e^x key followed by the →R key.
The method described should prove especially useful for calculations involving the complex numbers occurring in ac circuit analysis. Certain standing wave calculations usually done with a Smith chart transmission-line calculator can also be carried out by evaluating the transmission-line equation directly. The time required is about the same for both methods, but the accuracy of the numerical calculation is much greater than that obtained with the Smith chart.

source: AJP Volume 42, COMPUTER NOTES, Complex Number Arithmetic with a Pocket Calculator, W. C. ELMORE (Swarthmore College), April 1974, pg. 340

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