HP 49g manual Chapter Calculations with complex numbers, Definitions

Chapter 4

Calculations with complex numbers

This chapter shows examples of calculations and application of functions to complex numbers.

Definitions

A complex number z is written as z = x + iy, (Cartesian form) where x and y are real numbers, and i is the imaginary unit defined by i2 = -1. The number has a real part, x = Re(z), and an imaginary part, y = Im(z). The polar form of a complex number is z = re iθ = r⋅cosθ + i r⋅sinθ, where r = z

= x 2 + y 2 is the modulus of the complex number z, and θ = Arg(z) =

arctan(y/x) is the argument of the complex number z. The complex conjugate of a complex number z = x + iy = re iθ, isz = x – iy = re -iθ . The negative of z, –z = -x-iy = - re iθ, can be thought of as the reflection of z about the origin.

Setting the calculator to COMPLEX mode

To work with complex numbers select the CAS complex mode:

H@@CAS@) ˜˜™@￿@CHK

The COMPLEX mode will be selected if the CAS MODES screen shows the option _Complex checked off, i.e.,

Press @@OK@@ , twice, to return to the stack.

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