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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. 3 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. 4