**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

Eddie,

ReplyDeleteDoes the complex exponential program return -1 for

e^(i*pi)? That would be a nice test for the program.

Hank

Typo: under Complex Exponential Function - Calculation, change e^(yi) to e^(bi).

Delete