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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.

TI-NSpire Calculator

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

Casio FX Calculator

Example 1

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

Keystrokes Display
`56` `56`
Polar to rectangular `56`
`27` `27`
equals button `49.89636535 (= x)`
x to y button `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`
rectangular to polar button `12`
`42` `42`
Plus/minus button `-42`
equals button `43.68065934 (= r)`
x to y button `-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.

Tips, tricks, lessons, and tutoring to help reduce test anxiety and move to the top of the class.