Download PreCal 6.5 Trigonometric Form of a Complex Number

PreCal 6.5 Trigonometric Form of a Complex Number ­ End.notebook
March 23, 2017
6-5 Trigonometric Form of a Complex Number
Recall from Algebra II Honors that
you can represent a complex number z = a + bi as the point (a, b) in a coordinate plane (the complex plane). The horizontal axis is called the real axis and the vertical axis is called the imaginary axis.
The absolute value of a complex number a + bi is defined at the distance between the origin (0, 0) and the point (a, b)
Ex. 1 Plot each complex number and find its absolute value.
A.
z = −2 + 5i B.
z = 3√2 − 7i 1
PreCal 6.5 Trigonometric Form of a Complex Number ­ End.notebook
March 23, 2017
Trigonometric Form of a Complex Number
To work effectively with powers and roots of complex numbers, it is helpful to write complex numbers in trigonometric form.
Ex. 2 Write the trigonometric form of the following complex numbers.
A.
−
z = −2 − 2√3i B.
z = −6 + 6i 2
PreCal 6.5 Trigonometric Form of a Complex Number ­ End.notebook
March 23, 2017
Ex. 3 Write the complex number in standard form a + bi.
A.
B.
Multiplication and Division of Complex Numbers
The trigonometric form adapts nicely to multiplication and division of complex numbers.
Note that this rule says that to multiply two complex numbers you multiply moduli and add arguments, whereas to divide two complex numbers you divide moduli and subtract arguments.
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PreCal 6.5 Trigonometric Form of a Complex Number ­ End.notebook
March 23, 2017
Ex. 4 Find the product z1z2 of the complex numbers.
A.
B.
Ex. 5 Find the quotient z1/z2 of the complex numbers.
A.
B.
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