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 ∠, press SHIFT (-)

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

Example

(2+i)4+(2−i)2=−4+20i

Complex number in polar form

Example

4∠45=(2+2i)×√2

The angle unit is DEG

Angle Unit See more details about Angle Units (DEG / RAD / GRA)

Press SHIFT (-) to enter polar ∠ operator

Argument of the complex number

Example

Arg(1+i)

1. Press SHIFT 2 to open Complex menu,

   then select the Arg item

   

2. Type the expression 1+i

   

Conjugate of the complex number

Example

Conjugate(2+5i)=2−5i

1. Press SHIFT 2 to open Complex menu,

   then select the Conjg item

   

2. Type the expression 2+5i

   

Absolute value of complex number

Example

∣2+5i∣=√29

1. Press SHIFT 2 to open Complex menu,

   then select the Abs item

   

2. Type the expression 2+5i

   

Converting complex number to polar form

Converting Complex To Polar Form See more about converting Complex to Polar form