Trigonometric Form of Complex Numbers 6 6 a

Trigonometric Form of Complex Numbers 6. 6 a The first stuff in our last section of the chapter!

But first, remind me – what’s a complex number? ? ? A complex number is one that can be written in the form where a and b are real numbers. The real number a is the real part, the real number b is the imaginary part, and a + bi is the standard form. And of course, remember the definition of the imaginary number:

In Sec. 6. 1, we learned how to write a vector in “trigonometric form”: Now, we will do something similar with complex numbers…

Recall how we graph complex numbers: Imaginary Axis P(a, b) z = a + bi r 0 a b Real Axis

Definition: Trigonometric Form of a Complex Number The trigonometric form of the complex number z = a + bi is The number r is the absolute value or modulus of z, and 0 is an argument of z. Is the argument of any particular complex number unique?

Practice changing forms of complex numbers Switch forms of the given complex number, for (between trigonometric form and standard form) How about a graph? ? ? Reference angle: so…

Practice changing forms of complex numbers Switch forms of the given complex number, for

Practice changing forms of complex numbers Switch forms of the given complex number, for In this case, simply evaluate the trigonometric functions…

Practice changing forms of complex numbers Switch forms of the given complex number, for

Practice changing forms of complex numbers Switch forms of the given complex number, for

Whiteboard Problems: Switch forms of the given complex number, for