Relations and Functions

Relations and Functions

Question

Write the following in the form a + ib.

space space space space fraction numerator left parenthesis 1 plus straight i right parenthesis squared over denominator 3 minus straight i end fraction


Answer
space space space space space space straight z space equals space fraction numerator left parenthesis 1 plus straight i right parenthesis squared over denominator 3 minus straight i end fraction equals fraction numerator 1 plus straight i squared plus 2 straight i over denominator 3 minus straight i end fraction equals fraction numerator 2 straight i over denominator 3 minus straight i end fraction equals fraction numerator 2 straight i over denominator 3 minus straight i end fraction straight x fraction numerator 3 plus straight i over denominator 3 plus straight i end fraction equals fraction numerator 6 straight i plus 2 straight i squared over denominator 9 minus straight i squared end fraction

  space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space space space space space fraction numerator negative 2 plus 6 straight i over denominator 10 end fraction equals fraction numerator negative 1 over denominator 5 end fraction plus 3 over 5 straight i space equals space straight a plus space ib
Where space space space space straight a space equals space fraction numerator negative 1 over denominator 5 end fraction comma space space straight b space equals space 3 over 5

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