Solve complex - Casio FX82ES Scientific Calculator

It does not solve complex number equations. You can do simple calculations on complex numbers: addition, multiplication, etc. But nothing fancy.

Is it complex or matrix? You can have only one mode at a time.What kind of equations? The solve function uses real-valued equations.
Complex numbers: You can add, subtract, multiply and divide. You can convert a number from rectangular to polar forms and vice-versa; you can calculate the absolute value of a complex number, or a conjugate.
All the operations are done in the Mode CMPLX.

See cap image below

Your scientific calculator is unable to solve complex equation with complex coefficients. You should try to solve by hand directly using the quadratic formula or by factoring the polynomial in z
failing that, another way would be to set z=x+iy, substitute this for z, carry out the algebra and try to separate real and imaginary parts. But your two equations will constitute a system of two quadratic equations. I am not aware of any general method to solve coupled nonlinear equations.
Good luck.

The Casio FX-9860G SD can solve a polynomial equation of degree 2 or 3 with REAL coefficients. If the complex MODE is set to REAL it will find the real roots. If the complex mode is set to a+ib, it will find the real and complex roots.

Apparently it will take coefficients that are real, and will give a Ma Error if any coefficient is complex.

Addendum.
The calculator CANNOT solve equations with complex coefficient. YOU can however convert the system of linear equations with ccomplex coefficients ( of the type you show) as a system of 4 linear equations in 4 unknowns; Split x into a real and an imaginary part, split y into a real and an imaginary part. Substitute Real(x)+iIm(x) for variable x in the equations; substitute Real(y)+iIm(y) for y in the two equations; do the algebra. In each of the original equations split the Real and imaginary parts. You should be able to derive 4 linear equations in unknowns Real(x), Im(x), Real(y), and Im(y).
Use the linear equation solver to obtain the solutions. Recompose x=Real(x)+iIm(x), and y=Real(y)+iIm(y)

Your question (?) is not clear so I will not try to guess what you really mean.
Be it as it may, the Casio FX-9860G SD can solve a polynomial equation of degree 2 or 3 with REAL coefficients. If the complex MODE is set to REAL it will find the real roots. If the complex mode is set to a+ib, it will find the real and complex roots.

Apparently it will take coefficients that are real, and will give a Ma Error if any coefficient is complex.

Your question (?) is not clear so I will not try to guess what you really mean.
Be it as it may, the Casio FX-9860G SD can solve a polynomial equation of degree 2 or 3 with REAL coefficients. If the complex MODE is set to REAL it will find the real roots. If the complex mode is set to a+ib, it will find the real and complex roots.

Apparently it will take coefficients that are real, and will give a Ma Error if any coefficient is complex.

"Is there anything that I can do about this to stop my answers being complex numbers when solving cubic equations?"
You are making an assumption that is unwarranted.Namely that a cubic equation must necessarily have 3 real roots. This is not the case.

Let your equation be

If coefficients are complex you should expect some complex roots. Right?
If the coefficients are REAL then depending on the discriminant

you can have three cases
DELTA positive : three distinct real roots
DELTA=0 , the equation has a multiple root and all roots are REAL
DELTA negative: the equation has ONE real root and 2 complex roots that are complex conjugate of each other.

It suffices to look at the Tartaglia/Cardano expressions of the roots to know that more often than not there is going to be complex roots.

Hello,
You perform all calculations in complex mode. When you need to convert to angle amplitude, in the [RUN] screen press [OPTN][F3:CMPLX]
To obtain the angle press [Arg] ( complex number) [EXE]
To obtain the magnitude, amplitude press [Abs] (complex number) [EXE].
Since the [ANS] memory keeps only the last value calculated, you may have to store your result (the complex number) in a variable.

1+ 1 i [white right arrow under tan key to store] [ALPHA] H
Display shows 1+1i. Then
[Abs] [ALPHA] H [EXE] gives 1.414213562
[Arg] [ALPHA] H [EXE] gives 45

Hope it helps.

Hello,
I do not understand what you mean by solve complex equations, but if you want to manipulate complex numbers here are the tools you need to enter your complex numbers. Operations and function evaluations do not need special symbols.

Hope it helps.