Complex Number Calculations (CMPLX)

To perform complex number calculations, first press (CMPLX) to enter the CMPLX Mode.

You can use either rectangular coordinates (a+bi) or polar coordinates (r∠θ) to input complex numbers.
Complex number calculation results are displayed in accordance with the complex number format setting on the setup menu.

Example 1: (2 + 6i) ÷ (2i) = 3 - i (Complex number format: a+bi)

26(i)2(i)
3-i

Example 2: 2∠45 = √2 + √2i (MthIO-MathO) (Angle unit: Deg)

(Complex number format: a+bi)

2(∠) 45
√2+√2i

Example 3: √2 + √2i = 2∠45 (MthIO-MathO) (Angle unit: Deg)

(Complex number format: r∠θ)

22(i)
2∠45

Note

If you are planning to perform input and display of the calculation result in polar coordinate format, specify the angle unit 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 Linear Display is selected will show a and bi (or r and θ) on separate lines.

CMPLX Mode Calculation Examples

Example 1: (1 - i)-1 = ¹₂ + ¹₂i (MthIO-MathO) (Complex number format: a+bi)

1(i)
¹₂+¹₂i

Example 2: (1 + i)2 + (1 - i)2 = 0 (MthIO-MathO)

1(i)1(i)
0

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

(Complex number format: a+bi)

(CMPLX)(Conjg) 23(i)
2-3i

Example 4: To obtain the absolute value and argument of 1 + i (MthIO-MathO) (Angle unit: Deg)

Absolute Value (Abs):

(Abs) 1(i)
√2

Argument (arg):

(CMPLX)(arg) 1(i)
45

Using a Command to Specify the Calculation Result Format

Either of two special commands (r∠θ or a+bi) can be input at the end of a calculation to specify the display format of the calculation results.
The command overrides the calculator's complex number format setting.

Example: √2 + √2i = 2∠45, 2∠45 = √2 + √2i (MthIO-MathO) (Angle unit: Deg)

22(i)(CMPLX)(r∠θ)
2∠45

2(∠) 45(CMPLX)(a+bi)
√2+√2i