Converting Complex Numbers

Polar to Rectangular Forms Using Calculator

Choosing a Calculator

The first example is applicable to most advanced calculators, while the second example is specific to Casio calculators. If you need help determining which calculator is best for you, see our review guide here: How to Buy a Calculator.

You can find our review of the Casio FX: Casio FX Calculator Review.

Example 1

Convert `56\ ∠\ 27^@` to rectangular form (x + jy), where `j=sqrt(-1)`.

Keystrokes	Display
`56`	`56`
	`56`
`27`	`27`
	`49.89636535 (= x)`
	`25.42346799 (= y)`

Therefore, `56\ ∠\ 27^@ ≈ 49.9 + 25.4 j`

We have converted a complex number from polar form (using degrees) into rectangular form.

Of course, you have to be careful that you have your calculator set correctly in degrees (or radians, if required).

Example 2

Convert `12 - 42j` to polar form (`r ∠ theta`).

For CASIO calculator...

Keystrokes	Display
`12`	`12`
	`12`
`42`	`42`
	`-42`
	`43.68065934 (= r)`
	`-74.0546041 (= θ)`

Therefore:

Complex number in rectangular form: `12 - 42j`

Same complex number in polar form: `43.7 ∠ -74^@`

For Sharp calculator, it is a similar process.

Consult your calculator manual for full details.