Casio FX-114 Polar Conversions and Usage

Example 1: Convert the complex number (z = -4+3i) into polar form.
1. In the COMPLEX Mode, set the angle unit to Degree (Deg).
  [MODE] [2](COMPLEX)
  [MODE]...[1](Deg)
2. Input the complex numbers  z=-4+3i.
  [(-)][4][+][3][ENG](i)[=]
3. The result in rectangular form.
  The value of real part:  -4
  The value of imaginary part after pressing [SHIFT][=] (Re<->Im):  3  (i)
4. The display change of the value of rectangular form is carried out at polar form.
  The absolute value of the number in polar form after pressing [SHFT][+](>r<θ)[=]: 5
  The angle value after pressing [SHFT][=] (Re<->Im): 143.1301024
The result in polar form :5<143.1301024 (Angle unit:Deg)

Example2: Convert the complex number (2<60º) into rectangular form.
1. In the COMPLEX Mode, set the angle unit to Degree (Deg).
  [MODE] [2](COMPLEX)
  [MODE]...[1](Deg)
2. Input the complex numbers  2<60.
  [2][SHIFT][(-)](<)[6][0][=]
3. The result in rectangular form.
  The value of real part:  1
  The value of imaginary part after pressing [SHIFT][=] (Re<->Im):  1.732050808 (i)
The result in rectangular form:  1+1.732050808i

It is possible to work with the angle unit Radian. When angle mode is set as Radian, the angle values can input as pi-Multipliers. (180º =π radian.)

Above Example2 is calculated in Radian.
1. In the COMPLEX Mode, set the angle unit to Radian(Rad).
 [MODE][2](COMPLEX)
 [MODE]...[2](Rad)
2.Input the complex numbers 2<π/3. (60º=π/3 radian.)
 [2][SHIFT][(-)](<)[SHIFT] [EXP](π)[ab/c] [3][=]
3. The result in rectangular form.
 The value of real part: 1
 The value of imaginary part after pressing [SHIFT][=] (Re<->Im):  1.732050808 (i)

Complex Numbers – Calculation (Addition / Subtraction)

The two rectangular form complex numbers z1 and z2 are given. :
z1 = 4+2i, z2 = -1+5i
Example 3: Addition   z1+z2=3+7i
1. In the COMPLEX Mode, set the angle unit to Degree (Deg).
  [MODE] [2](COMPLEX)
  [MODE]...[1](Deg)
2. Input the value.  z1+z2.
Displayed Result:
 The value of real part: 3
 The value of imaginary part after pressing [SHIFT] [=](Re<->Im):  7  (i)


Example4: Subtraction  z1-z2=5-3i
1. In the COMPLEX Mode, set the angle unit to Degree (Deg).
  [MODE] [2](COMPLEX)
  [MODE]...[1](Deg)
2. Input the value.  z1-z2.
Displayed Result:
 The value of real part: 5
 The value of imaginary part after pressing [SHIFT] [=](Re<->Im):  -3  (i)


Complex Number – Calculation (Multiplication / Division)

The two polar form complex numbers z1 and z2 are given.(Angle unit:Degree):
 z1 =5<70, z2 = 3<45

Example 5:  Multiplication z1*z2=15<115
1. Set the complex mode, the polar form for display of complex number calculation results and the angle unit Degree in setting.
  [MODE][2](COMPLEX)
  [MODE]...[1](Disp)[right cursor key][2](r<θ)
  [MODE]...[1](Deg)
2.Input the value. z1*z2
Displayed Result:
 The absolute value of the number in polar form : 15
 The angle value after pressing [SHFT][=] (Re<->Im): 115

Example6: Division  z1/z2= 1.666666667< 25
 1. Set the complex mode, the polar form for display of complex number calculation results and the angle unit Degree in setting.
  [MODE][2](COMPLEX)
  [MODE]...[1](Disp)[right cursor key][2](r<θ)
  [MODE]...[1](Deg)
2.Input the value. z1/z2
Displayed Result:
 The absolute value of the number in polar form : 1.666666667
 The angle value after pressing [SHFT][=] (Re<->Im): 25

3.The display change of the value of polar form is carried out at rectangular form.
 The value of real part after pressing [SHIFT][-](>a+bi)[=]: 1.510512978
 The value of imaginary part after pressing [SHIFT][=](Re<->Im): 0.704363769 (i)