Texas Instruments TI-89 User Manual - Page 799

cSolve() temporarily sets the domain to complex during the solution even if the current domain is real. In the complex domain, fractional powers having odd denominators use the principal rather than the real branch. Consequently, solutions from solve() to equations involving such fractional powers are not necessarily a subset of those from cSolve(). cSolve() starts with exact symbolic methods. Except in EXACT mode, cSolve() also uses iterative approximate complex polynomial factoring, if necessary. Note: See also cZeros(), solve(), and zeros(). Note: If equation is non-polynomial with functions such as abs(), angle(), conj(), real(), or imag(), you should place an underscore (¥ ) at the end of var. By default, a variable is treated as a real value. If you use var_ , the variable is treated as complex. You should also use var_ for any other variables in equation that might have unreal values. Otherwise, you may receive unexpected results. cSolve(x^(1/3)=ë 1,x) ¸ solve(x^(1/3)=ë 1,x) ¸ Display Digits mode in Fix 2: exact(cSolve(x^5+4x^4+5x ^3ì6xì3=0,x)) ¸ cSolve(ans(1),x) ¸ z is treated as real: cSolve(conj(z)=1+ i,z) ¸ z_ is treated as complex: false x = ë1 z=1+ i cSolve(conj(z_)=1+ i,z_) ¸ z_=1− i cSolve(equation1 and equation2 [and ... ], {varOrGuess1, varOrGuess2 Boolean expression Returns candidate complex solutions to the simultaneous algebraic equations, where each varOrGuess specifies a variable that you want to solve for. Optionally, you can specify an initial guess for a variable. Each varOrGuess must have the form: variable - or - variable = real or non-real number For example, x is valid and so is x=3+i. If all of the equations are polynomials and if you do NOT specify any initial guesses, cSolve() uses the lexical Gröbner/Buchberger elimination method to attempt to determine all complex solutions. Complex solutions can include both real and nonreal solutions, as in the example to the right. Note: The following examples use an underscore (¥ ) so that the variables will be treated as complex. cSolve(u_ùv_ìu_=v_ and v_^2=ëu_,{u_,v_}) ¸ u_=1/2 + 23øi and v_=1/2 ì 23øi or u_=1/2 ì 23øi and v_=1/2 + 23øi or u_=0 and v_=0 Appendix A: Functions and Instructions 799