Question

Express the following complex numbers in the x + iy form. Try to visualize each complex number, using sketches as in the examples if necessary. The first twelve problems you should be able to do in your head (and maybe some of the others—try it!) Doing a problem quickly in your head saves time over using a computer. Remember that the point in doing problems like this is to gain skill in manipulating complex expressions, so a good study method is to do the problems by hand and use a computer to check your answers.

1) e-ᶦπ/⁴

Answer 1

To express the complex number e^-iπ/4 in the x + iy form, we can use Euler's formula.

Step-by-step explanation:

To express the complex number e-iπ/4 in the x + iy form, we can use Euler's formula, which states that eix = cos(x) + i sin(x). In this case, we have x = -π/4. Substituting this into the formula, we get:

e-iπ/4 = cos(-π/4) + i sin(-π/4)

= √(2)/2 - i √(2)/2