## TiNspire : Solve Complex Numbers and Complex Functions

TiNspire users can solve Complex Numbers and Complex Functions – Step by Step – using the Complex Analysis Made Easy app at www.TiNspireApps.com :

The App is comprehensive and capabilities can be viewed below, the free trial can be downloaded at www.TinspireApps.com/trials

Capabilities:

• Step by Step Complex Numbers
• Step by Step Analytic and Harmonic Functions
• Step by Step Cauchy-Riemann Conditions
• Step by Step Solve Contour Integrals
• Step by Step Poles and their Order
• Step by Step Residues and their Sums
• Step by Step Solve Complex Equations
• Step by Step Solve Quadratic Equations
• Step by Step Differentiation and Integration
• Solve any Equation or Inequality
• One Complex Number: All-in-one-Explorer
• Two Complex Numbers: All-in-one-Explorer
• De Moivre Theorem : (a+bi)^n
• De Moivre Theorem : r*(cos(x)+sin(x)*i)^n
• Roots of Unity : z^n=1
• Remainder Theorem
• Find Partial Fractions
• Factor
• Expand/Distribute
• Evaluate f(z)
• Find Poles of f(z)
• Find the Order of Poles of f(z)
• Pole-Zero Plot
• Find Residues of f(z) and their Sum
• Find Limits: lim z->c f(z)
• Compute Discriminant
• Complete the Square
• Complete the Square to find Zeros
• Complete the Square to find Vertex
• Is Complex f Analytic?
• Check Cauchy-Riemann Conditions
• Is f Harmonic?
• Find the Harmonic Conjugate Function
• Find f'(z) and f”(z)
• Evaluate f'(z) and f”(z)
• Step by Step Differentation
• Find Laurent Series at Poles
• Find Integral f(z)dz
• Find Definite Integral (z)dz over [z1,z2]
• Find Contour Integral Integral f(z)dz
• Find Curve Integral Integral f(z)dz
• Find Antiderivative & Constant of Integration: Integral f(x)dx + C
• Step by Step Integration: Integral f(x)dx
• Laplace Transforms
• Solve 2. order Diff Eq using Laplace Transforms
• Solve 3. order Diff Eq using Laplace Transforms
• Table of Laplace Transforms
• Inverse Laplace Transform
• Fourier Transform of Piecewise Def Function
• Fourier Transform of f(t)
• Inverse Fourier Transform
• Table of Fourier Transforms
• Table of Z-Transforms
• Solve any 1. order Differential Equation
• M(x,y)dx+N(x,y)dy=0
• Linear in y Differential Equation
• Newtons Law of Cooling / Heating
• Euler Method given n=Number of Pts.
• Solve any 2. order D.E.
• Homogeneous Differential Equation
• Non-Homogeneous Differential Equation
• All in one Vector Explorer
• Find Norm
• All in one 2-Vectors Explorer
• Find Angle between 2 Vectors
• Find Cross Product
• Laplacian of Scalar Field
• Divergence of a 3D Vector Field
• Curl of a 3D Vector Field
• Line Integral Integral(f1dx+f2dy) over Curve C
• Area under Param. Curve using Line Integral
• Line Integral given Function & Parametrization
• Line Integral given Function & 2 Points
• Line Integral given Vector Field & Parametriz.
• Greens Theorem Integral(Pdx+Qdy)
• Greens Theorem Integral(Pdy+Qdx)
• Surface Integral: Function
• Surface Integral: Function & t-u-Parametrization
• Surface Integral: Vector Field

## TiNspire : Complex Analytic and Harmonic Functions

In Complex Analysis you will be asked to check if a complex function is analytic which requires checking the 2 Cauchy Riemann Conditions. Fortunately, the TiNspire has the ability to deal with those and we can go ahead and solve those problems using the Complex Analysis Made Easy app at www.TinspireApps.com to solve those problems step by step.

Say we are given a complex valued function in the format u+i*v such as x^2-y^2+i*2*x*y as shown below. Out comes the solution with steps showing that this function is indeed analytic. Insiders realize that this is actually the function f(z)=z^2

When entering z^2 in the top box we will get naturally the same answer. See below

Next Question: Is a given Complex Function Harmonic? And if so what is its harmonic conjugate ?

Lets select that option in the menu as shown below:

Lets answer the first question first : Is e^(-3x)*cos(3y) harmonic ? Well, let’s just enter it as shown below:

Voila! It is Harmonic. And we understand why 😉

Lastly, let’s find the harmonic conjugate function to x^2-y^2 , entered as shown below:

Beautiful, good thing we have our handy dandy TiNspire to provide those answers.