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# Online Tutorial - CG50: How to Work with Complex Numbers

## Video Transcript

In this tutorial we'll be looking at how to use complex numbers in run mode and how to set the calculator to give complex roots of equations in equation mode. To work along with this tutorial, you may find it easiest to reset your calculator before starting so that the screen matches the one in the video.

Notice the default setting for the CG50 is real. In run mode, type the square root of -1 and execute. So the default setting of real makes an error message appear here. To the complex answer, we need to change the settings. Exit the error screen and go to setup. Scroll down and switch to a plus bi and execute. And now when you execute the calculation, there's no need to type it again, and a complex answer is given.

The menu for complex numbers is under option, complex numbers. Use the fraction template to type the expression and use F1 to type in the i. Use the cursor down to get to the denominator and execute to simplify the expression. Use absolute value for the modulus and the more familiar notation appears on the screen. Type the number and execute. Notice there are two screens of functions available in the complex mode. Now the calculator is set to working complex numbers, equation mode will produce complex roots for polynomial equations with real coefficients. From the main menu. Go to equation mode, choose polynomial degree two. Type in the coefficients one, two and five into the matrix. And then solve.

To solve a cubic equation, go back through the menus and choose polynomial degree three. Type the coefficients do take care here that the constant term needs to be on the left hand side of the equation, so we need the -1 here. And solve. You can scroll down to see the complex roots in surd form. If you exit and change the settings, you can see the roots in polar fall.

Notice here that the angle setting is radians and you can move the cursor down to see the argument as a multiple of Pi. You can find additional resources at education.casio.co.uk.