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Trigonometric Form of Complex NumbersSummary of U4 L2 I1
Graphical Representation of a Complex NumberGraph in coordinate plane Called the complex plane Horizontal axis is the real axis Vertical axis is the imaginary axis 3 + 4i • -2 + 3i • • -5i
Absolute Value of a Complex NumberDefined as the length of the line segment From the origin To the point Calculated by using Pythagorean Theorem 3 + 4i •
Find That Value, AbsolutelyTry these Graph the complex number Find the absolute value
Trig Form of Complex NumberConsider the graphical representation We note that a right triangle is formed a + bi • r b θ a How do we determine θ?
Trig Form of Complex NumberNow we use and substitute into z = a + bi Result is Abbreviation is often
Try It Out Given the complex number -5 + 6i Given z = 3 cis 315°Write in trigonometric form r = ? θ = ? Given z = 3 cis 315° Write in standanrd form a = ? b = ?
Product of Complex Numbers in Trig FormGiven It can be shown that the product is Multiply the absolute values Add the θ's
Quotient of Complex Numbers in Trig FormGiven It can be shown that the quotient is
Try It Out Try the following operations using trig formConvert answers to standard form
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