How do I enter pi on Casio fx-115es?

Press [SHIF][X10^x]. If it is displayed as the Greek letter Pi, you can still use it as is in calculations.
Please read the manual, it will prove worthwhile.

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.

This calculator cannot manipulate algebraic expressions. You can enter an expression and generate a table of values. You can enter an equation in one unknown and solve it. But you cannot do algebra.
You would need a calculator that has a Computer Algebra System (Algebra FX 2.0, or ClassPad 300/330). Sorry.

You do not need a calculator for this proportion.
For a proportion a/b=c/d, the product of the extrems (a*d) is equal to the product of the means (b*c).
In your case x*x=8*8 or x^2=64.
The two solutions are x=+square root (64) or x=-square root(64).

For a less trivial equation, you can use the solve feature of the FX-119ES. To do so, use the ALPHA keyboard to enter your equation; once the equation is typed in, do not press the main equal sign, but the Solve key (the key is located near the top left corner of the keyboard). You will be prompted to solve for X?.

It is always risky to try to answer a question about a calculator of an undisclosed model.
To be able to symbolic algebra (with variables), one needs a calculator with CAS (or Computer Algebra System). These types of calculators are special graphing calculators. ( Not all graphing calculators have a CAS.)

To get back to your question: No, you cannot do algebra with a mere scientific calculator even a recent one. All you can do is define an equation with variables A,B,C,D, Y and X and press the Solve button if it exists. The calculator will ask: Solve for X?. If you say yes, you will be prompted for the values of all letters (A,B,C,D, Y) in your equation and the calculator will search for the value of X, that makes the left side of your equation equal to the right side.

It will display the X-value and the difference L-R.

No, your calculator cannot factor polynomials. You need a calculator that has a CAS (computer Algebra System)
Yes Casio sells calculators with CAS: The FX-Algebra 2.0 and 1.0, the FX-9860GPLUS/GII SD, the GRAPH85 or 80 and the Graph 100+. You also have the CLASSPAD Series 300PLUS and 330.
TI and HP also have CAS calculators.

Texas Instruments
TI 89 /Titanium, Voyage 200PLT, TI92PLUS (discontinued), TI Inspire CAS.

Hewlet-Packard
HP 48G/G+/GX, HP40G, HP49G/G+ and the top of the line HP50G

You can use symbols (X,Y,A,B,C,D, and M, =) to create expressions to use in the SOLV program or to generate a table of values.

To type them you use [ALPHA] followed by the symbol you want. The symbols on the body of the calculator are of the same color as the ALPHA key. The [=] in expressions is different from the general = sign at the bottom of the keypad.

There are also some typical equations already in the calculator: simultaneous linear equation in 2 or 3 unknowns, and polynomial equations of 2nd and 3rd degree. They are accessed under the EQUATion Mode.

To input an = sign use: alpha, calc

Use the key that is 3 keys below the ALPHA button. You must press that key, then place the number or equation you are trying to get the square root of.

cryshug24 the mode(s) you want to use is mth IO and line IO for algebra. push the shift mode then #1. to write out a long equation push shift mode #2. you have to keep playing between the two modes to get the correct answer.