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.
Use Radian mode.
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
Rad
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
Rad
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
Rad
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
