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Published byMaximillian Lain Modified over 2 years ago

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Trigonometric Form of Complex Numbers Summary of U4 L2 I1

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2 Graphical Representation of a Complex Number Graph in coordinate plane Called the complex plane Horizontal axis is the real axis Vertical axis is the imaginary axis 3 + 4i -2 + 3i -5i

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3 Absolute Value of a Complex Number Defined as the length of the line segment From the origin To the point Calculated by using Pythagorean Theorem 3 + 4i

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4 Find That Value, Absolutely Try these Graph the complex number Find the absolute value

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5 Trig Form of Complex Number Consider the graphical representation We note that a right triangle is formed a + bi θ b a r How do we determine θ?

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6 Trig Form of Complex Number Now we use and substitute into z = a + bi Result is Abbreviation is often

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7 Try It Out Given the complex number -5 + 6i Write in trigonometric form r = ? θ = ? Given z = 3 cis 315° Write in standanrd form r = ? a = ? b = ?

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8 Product of Complex Numbers in Trig Form Given It can be shown that the product is Multiply the absolute values Add the θ's

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9 Quotient of Complex Numbers in Trig Form Given It can be shown that the quotient is

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10 Try It Out Try the following operations using trig form Convert answers to standard form

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