Transcription of 1. CARTESIAN COMPLEX NUMBERS
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1. CARTESIAN COMPLEX NUMBERS
UNIVERSITI KUALA LUMPUR COMPLEX number E2 1. CARTESIAN COMPLEX NUMBERS INTRODUCTION Try to solve this quadratic equation : 0522=++xx By using quadratic formula : the discriminant , 16)5)(1(4)2(422 = = = acb the solution : )1(216)2( =x but it is not possible to evaluate 1 however if an operator j is defined as then the solution may be expressed as : 12 =j 21242)1(216)2(jjx = = = 21j+ and are known as COMPLEX NUMBERS . 21j Both solutions are of the form : = x1 2j COMPLEX number Real part Imaginarypart z = ajb this form is known as the CARTESIAN COMPLEX NUMBERS ( ALGEBRAIC FORM ) E2 - 1 - MATHEMATICS UNIT UNIVERSITI KUALA LUMPUR COMPLEX number E2 EXAMPLES EXAMPLE 1 : Solve the quadratic equation , 042=+x 240422jxxx = ==+ EXAMPLE 2 : Solve the quadratic equation , 2 x 2 + 3 x + 5 = 0 2343463436344093)2(2)5)(2(4332jxjxxxx = = = = = E2 - 2 - MATHEMATICS UNIT UNIVERSITI KUALA LUMPUR COMPLEX number E2 POWERS OF j j 0 0)1( 1 j 1 1 j j 2 )1)(1( -1 j 3 j2j = (-1)j -j j 4 j2j2 = (-1)(-1) 1 j 5 j4j = (1)j j In general we can bri
Two complex numbers are added / subtracted by adding / subtracting separately the two real parts and two imaginary parts . Given two complex number Z = a + j b and W = c + j d 2.1 IDENTITY If two complex numbers are equal , then their real parts are equal and their imaginary parts are equal .
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