Computing Complex Math

Python
import cmath

# Basic operations
cmath.sqrt(-1)              # 1j
cmath.exp(1j * cmath.pi)    # -1+1.2246e-16j (Euler's identity)
cmath.log(1j)               # 1.5707963267948966j

# Polar conversion
z = 3 + 4j
r, phi = cmath.polar(z)     # (5.0, 0.9272952180016122)
z2 = cmath.rect(r, phi)     # (3+4j) reconstructed

Progress:

• Identify if input/output involves complex numbers (vs. real-only math module)
• Choose the right function category (conversion, power/log, trig, hyperbolic, classification)
• Handle edge cases (infinities, NaN) if inputs may be non-finite
• Verify results with isclose() instead of == for float comparisons

Function Categories

Conversions to/from polar coordinates:

Python
cmath.phase(z)          # argument (angle) of z, range (-pi, pi]
cmath.polar(z)          # returns (r, phi) tuple
cmath.rect(r, phi)      # builds complex number from polar coords

Power and logarithmic functions:

Python
cmath.exp(z)            # e**z
cmath.log(z)            # natural log; cmath.log(z, base) for other bases
cmath.log10(z)          # base-10 log
cmath.sqrt(z)           # square root, principal branch

Trigonometric functions:

Python
cmath.sin(z), cmath.cos(z), cmath.tan(z)
cmath.asin(z), cmath.acos(z), cmath.atan(z)

Hyperbolic functions:

Python
cmath.sinh(z), cmath.cosh(z), cmath.tanh(z)
cmath.asinh(z), cmath.acosh(z), cmath.atanh(z)

Classification functions:

Python
cmath.isfinite(z)       # True if both real and imag parts finite
cmath.isinf(z)          # True if either part is infinite
cmath.isnan(z)          # True if either part is NaN
cmath.isclose(a, b, rel_tol=1e-09, abs_tol=0.0)  # safe comparison

Constants:

Python
cmath.pi, cmath.e, cmath.tau, cmath.inf, cmath.infj, cmath.nan, cmath.nanj