Converting Complex Numbers

Polar to Rectangular Forms Using Calculator

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.