Complex Number Calculation

CalcES calculator fully supports complex numbers and operations on complex numbers.

Inputting complex numbers

• To enter imaginary i, press SHIFT ENG
• To enter polar symbol ∠, pressSHIFT (-)

The complex menu

Press SHIFT 2 to open the complex menu. There are some builtin functions and operations:

• Arg(z): Argument of the complex number
• Conjg(z): Conjugate of the complex number
• Re(z): Real component
• Im(z): Imaginary component
• ►r∠φ Displays the result in polar form.
• ►a+bi: Displays the result in rectangular form.
• Abs(z): Returns the magnitude (modulus).

Calculation examples

Adding complex numbers

(1 + i)^4 + (1 - i)^2 = -4 + 20i

Complex number in polar form

The angle unit is DEG, see Angle Units

4∠45 = (2 + 2i)*Sqrt(2)

Press SHIFT (-) to enter polar ∠ operator

Argument of the complex number

Arg(1+i)

Press SHIFT 2 to open Complex menu, then select the Arg item

Type the expression 1+i

Conjugate of the complex number

Conjugate(2+5i) = 2 - 5i

Press SHIFT 2 to open Complex menu, then select the Conjg item

Enter 2+5i:

Absolute value of complex number

|2+5i| = Sqrt(29)

Press SHIFT 2 to open Complex menu, then select the Abs item

Enter 2 + 5i:

Converting complex number to polar form

See Converting Complex To Polar Form