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CLASE 13

CLASE 13. FORMA TRIGONOMÉTRICA DE LOS NÚMEROS COMPLEJOS. Tenemos. cos . a. b. =. =. . . (a;b). b. a. a=  cos . b=  sen . a <0. b >0. I. z=a+b i. z. sen . . IIC. .  cos .  sen . o. . + i. =. z =  c i s . cos  + i sen . z =  ( ).

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CLASE 13

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  1. CLASE 13

  2. FORMA TRIGONOMÉTRICA DE LOS NÚMEROS COMPLEJOS

  3. Tenemos cos a b = =   (a;b) b a a= cos b= sen a<0 b>0 I z=a+bi z . sen  IIC   cos  sen o  +i = z= ci s cos +i sen z=( ) abreviada Forma trigonométrica o polar.

  4. Expresa en forma trigonométrica tan 43 –4 3 3 =  = =a +b 2 2 = I z  a= –4 z = –4+4i3 II C b=43  z = 8ci s 120o z = 8(cos120o +i sen120o) 2 2 =(–4) +(43) b a =16+163 tan = =416 z=(cos +i sen)  =180o –  o polar el número complejo: o .  =60o = 24 =180o – 60o = 8 = 120o

  5. Expresa en forma binómica el número complejo z = 3 c s300o z= 3 (i ) z = 3 (cos300o+i sen300o) z = i 1 2 1 2 = 3 2 – 3 2 3 2 – 3 2 = – i IV C cos(360o–) = cos  cos300o = cos(360o–60o) = cos60o . sen(360o–)= – sen  sen300o = sen(360o–60o) = –sen 60o a>0 b<0

  6. . z4= 5 ci s0 z3=100 ci s 337o 7,4ci s90o 62(cos225o+i sen225o) 92–39i 5 ESTUDIO INDIVIDUAL a) Expresa en forma trigonométrica z1= –6–6i z2= 7,4i b) Expresaen forma binómica

  7. =a +b 2 2 I a=0 b=–5 =0 +(–5) 2 2 R z=5(cos 270o+i sen 270o) b a =25   =270o =90o tan = no –5 0 = Llevar a la forma trigonométrica definida el número complejo z –5i = .  z=–5i  = 5

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