## Thursday, March 3, 2016

### Casio fx-5800p: Complex Numbers Calculations: e^z, ln z, z^w

Casio fx-5800p:  Complex Numbers Calculations: e^z, ln z, z^w

Let z = a + bi = r*e^(θi) and w = c + di = s*e^(αi) where i = √-1

The complex mode of the Casio fx-5800p, and quite frankly, most graphing calculators of Casio have limited capabilities working with complex numbers, limited to arithmetic, and powers to real numbers only.  These three programs extend that functionality.

Complex Exponential Function

Calculation:  e^z = e^a * e^(yi) = e^a * (cos b + i*sin b)

The input is stored in Z, output is stored in X.

Program EXPCOMPLX
“Z”? → Z
ReP(Z) → A
ImP(Z) → B
e^(A)*(cos(B)+i*sin(B))→X

Examples:
e^(-6i) ≈ 0.9601702867 + 0.2794154982i
e^(5.25 + 3.75i) ≈ -156.3709348 – 108.9203077i

Complex Natural Logarithm Function

Calculation: ln z = ln r + iθ

Program LNCOMPLX
“Z”? → Z
Abs(Z) → R
Arg(Z) → T
ln(R) + iT → X

Examples:
ln(3 + 6i) ≈ 1.903331245 + 1.107148718i
ln(7i) ≈ 1.945910149 – 1.570796327i

Complex Power

Calculation: z^w = e^(w ln z)

Program POWCOMPLX
“Z^(W), Z”? → Z
Abs(Z) → R
Arg(Z) → T
ln(R) + iT → X
“W”? → W
WX → X
ReP(X) → A
ImP(X) → B
e^(A)*(cos(B) + i*sin(B)) → X

Examples:
(2 + 3i)^(-1 + i) ≈ 0.09917578259 + 0.03064399883i
(0.075 – 3i)^(0.2i) ≈ 1.3295102 + 0.2970040915i

This blog is property of Edward Shore - 2016