Any way to speed up calculation of a large complex exponential? (2025)

FAQs

What is the formula for complex to exponential? ›

The exponential form of a complex number is in widespread use in engineering and science. Since z = r(cosθ + isinθ) and since eiθ = cosθ + isinθ we therefore obtain another way in which to denote a complex number: z = reiθ, called the exponential form.

The exponential function is a basic building block for solutions of ODEs. Complex numbers expand the scope of the exponential function, and bring trigonometric functions under its sway.

The steps for multiplying complex numbers are: Step 1: Apply the distributive property and multiply each term of the first complex number with each term of the second complex number. Step 2: Simplify i² = -1. Step 3: Combine real parts and imaginary parts and simplify them to get the product.

a = the Real Part of z = Re(z), b = the Imaginary Part of z = Im(z). Note that both Rez and Imz are real numbers. A common mistake is to say that Imz = bi.

Early applications of eiωt in the context of electromagnetism were understood as a mathematical device: the physical fields are real, and the complex exponential is a convenient method to implement trigonometric relations.

Step 1: Isolate the exponential expression. Step 2: Take the natural log of both sides. Step 3: Use the properties of logs to pull the x out of the exponent. Step 4: Solve for x.

To solve an equation that has a complex number as a solution: Work with the purely real valued terms until no further simplification can be done and all that remains is an answer involving a negative radicand. Rewrite the complex root as the square root of a real number times the square root of -1.

The exponential growth and decay gives the required needed calculations using the formulas f(x) = a(1 + r)^t, and f(x) = a(1 - r)^t. Here a is the initial quantity, r is the growth or decay constant, and t is the time period or the time factor.

To add two complex numbers , add the real part to the real part and the imaginary part to the imaginary part. To subtract two complex numbers, subtract the real part from the real part and the imaginary part from the imaginary part. To multiply two complex numbers, use the FOIL method and combine like terms .