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COMPLEX NUMBERS EXAMPLES & SOLUTIONS

Producedby The Open University of Sri Lanka20150 COMPLEXNUMBERSEXAMPLES& SOLUTIONSD epartment of Mathematics & PhilosophyThe Open University of Sri LankaProducedby The Open University of Sri Lanka20151 EXAMPLES for COMPLEX numbersQuestion(01)(i) Find the real values ofxandysuch that(1)2(2 3 )33i xii y iiii ++++= +(ii)Find the real values ofxandyare the COMPLEX numbers23ix y and24xyi conjugate of each other.(iii)Find the square roots of4 4i+(iv)Find the COMPLEX numberZsatisfying the equation12583 ZZi = and418ZZ = (v) Find real such that3 21 2 sini sini + is(a) real(b) imaginarySolution(i)(1)2(2 3 )33i xii y iiii ++++= +{}{}(1)2 (3)(2 3 )(3)(3)(3)i xiii y iiiii ++ +++ = +222(3)(1)62(2 3 )(3)39ii xiiii yi iii+ ++++ + = 222(33)6(6 923 )39 1ii i xiiii yi ii+ +++ ++= +(4 2 )(9 7 )9110i xi yii + + = COMPLEX NUMBERS : EXAMPLES & SOLUTIONS

Examples for Complex numbers Question (01) (i) Find the real values of x and y such that (1 ) 2 (2 3 ) 3 3 i x i i y i i i i − + + + + =− − + (ii) Find the real values of x and y are the complex numbers 3−ix y2 and − − −x y i2 4 conjugate of each other. (iii) Find the square roots of 4 4+i (iv) Find the complex number Z satisfying ...

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