Trigonometric Form of Complex NumbersGraphical Representation of a Complex NumberAbsolute Value of a Complex NumberFind That Value, AbsolutelyTrig Form of Complex NumberSlide 6Try It OutProduct of Complex Numbers in Trig FormQuotient of Complex Numbers in Trig FormSlide 10AssignmentTrigonometric Form of Complex NumbersLesson 5.22Graphical Representation of a Complex NumberGraph in coordinate planeCalled the complex planeHorizontal axisis the real axisVertical axis is the imaginaryaxis3 + 4i•-2 + 3i •• -5i3Absolute Value of a Complex NumberDefined as the length of the line segmentFrom the originTo the pointCalculated byusing PythagoreanTheorem3 + 4i•2 23 4 3 4 25 5i+ = + = =4Find That Value, AbsolutelyTry theseGraph the complex numberFind the absolute value4 4z i= -5z =-5 6z i=- -5Trig Form of Complex NumberConsider the graphical representationWe note that a righttriangle is formeda + bi•θ2 2cos sincos sinwherea br ra r b rr z a bq qq q= == == = +barHow do we determine θ?How do we determine θ?1tanbaq-=6Trig Form of Complex NumberNow we use and substitute into z = a + biResult isAbbreviation is oftencos sina r b rq q= =cos sinz r i rq q= � + ��cisz r q= �7Try 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 = ?8Product of Complex Numbers in Trig FormGivenIt can be shown that the product isMultiply the absolute valuesAdd the θ's( ) ( )1 1 1 1 2 2 2 2cos sin cos sinz r i z r iq q q q= + � = + �( )1 2 1 2 1 2cisz z r r q q� = � � +9Quotient of Complex Numbers in Trig FormGivenIt can be shown that the quotient is( ) ( )1 1 1 1 2 2 2 2cos sin cos sinz r i z r iq q q q= + � = + �( )1 11 22 2cisz rz rq q= � -10Try It OutTry the following operations using trig formConvert answers to standard form( ) ( )4 cis120 6 cis315� � �o o15cis2403cis135oo11AssignmentLesson 5.2Page 349Exercises 1 – 61