You can use either rectangular coordinates (a+bi) or polar coordinates (r∠θ) to input complex numbers.

Example 1: To input 2+3i

• 23(i)*
• 

* You can also use the following operation to input i: – [Complex] > [i].

Example 2: To input 5∠30

• 5 – [Complex] > [∠] 30
• 

Before Performing the Example Operations

For the examples in this section, use the SETTINGS menu to select MathI/MathO for the Input/Output setting. Configure other settings as shown for each example.

Complex number calculation results are displayed in accordance with the Complex Result setting on the SETTINGS menu.

If you are planning to perform input and display of the calculation result in polar coordinate format, specify the Angle Unit on the SETTINGS menu before starting the calculation.

The θ value of the calculation result is displayed in the range of -180° < θ ≤ 180°.

Display of the calculation result while something other than MathI/MathO is selected will show a and bi (or r and θ) on separate lines.

Example 3: (1 + i)4 + (1 - i)2 = -4 - 2i

(Complex Result: a+bi)

• 1(i)4
  1(i)
• 

Example 4: 2∠45 = √2 + √2i

(Angle Unit: Degree, Complex Result: a+bi)

• 2 – [Complex] > [∠] 45
• 

Example 5: √2 + √2i = 2∠45

(Angle Unit: Degree, Complex Result: r∠θ)

• 22(i)
• 

Example 6: To obtain the conjugate complex number of 2 + 3i

(Complex Result: a+bi)

• – [Complex] > [Conjugate]
  23(i)
• 

Example 7: To obtain the absolute value and argument of 1 + i

(Angle Unit: Degree)

• – [Numeric Calc] > [Absolute Value]
  1(i)
• 

• – [Complex] > [Argument]
  1(i)
• 

Example 8: To extract the real part and imaginary part of 2 + 3i

• – [Complex] > [Real Part]
  23(i)
• 

• – [Complex] > [Imaginary Part]
  23(i)
• 

Converting a Complex Number Calculation Result to Rectangular or Polar Coordinates

You can use the FORMAT menu that appears when you press to convert a complex number calculation result to rectangular coordinate or polar coordinate format.

Example 9: √2 + √2i = 2∠45, 2∠45 = √2 + √2i

(Angle Unit: Degree, Complex Result: a+bi)

• 22(i)
• 

• – [Polar Coord]
• 

• – [Rectangular Coord]
• 

After enabling Verify in the Complex app, you can determine if an equation or inequality is true. With the Complex app, you can determine whether an equation that includes a complex number is true or false.

Example Verify Operation

Example 10: To determine whether i2 = -1 is true

1. To enable Verify, press and then select [Verify ON].

2. Input i2 = -1 and determine if it is true.

3. To disable Verify and exit the Verify operation, press and then select [Verify OFF].