### 5.55.7 Equation solving in ℂ : cSolve

cSolve takes two arguments and solves an equation or a system of polynomial equations.

- solving an equation
  cSolve takes as arguments an equation between two expressions or an expression (=0 is omitted), and a variable name (by default x).
  cSolve solves this equation in ℂ even if you are in real mode.
- solving a system of polynomial equations
  cSolve takes as arguments two vectors : a vector of polynomial equations and a vector of variable names.
  cSolve solves this equation system in ℂ even if you are in real mode.

Input :

cSolve(x`^`4-1=3)

Output :

[sqrt(2),-(sqrt(2)),(i)*sqrt(2),-((i)*sqrt(2))]

Input :

cSolve([-x`^`2+y=2,x`^`2+y],[x,y])

Output :

[[i,1],[-i,1]]