HP 48gII Calculations with complex numbers, Chapter, @@OK@@, Definitions, H@@CAS@) 2˜˜™@@CHK@, Setting the calculator to COMPLEX mode

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 representation) 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 representation of a complex number is z = re iθ = r⋅cosθ + i r⋅sinθ,

where r = z = x2 + y 2 is the magnitude 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@) 2˜˜™@@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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