Relations and Functions

Relations and Functions

Question

Write the following in the form a + ib.

space space space space space space fraction numerator 1 over denominator 3 space plus space 4 straight i end fraction

Answer
space space space space space space space space space space space space space z space equals space fraction numerator 1 over denominator 3 space plus space 4 i end fraction equals fraction numerator 1 over denominator 3 plus 4 i end fraction x fraction numerator 3 minus 4 i over denominator 3 minus 4 i end fraction equals fraction numerator 3 minus 4 i over denominator 9 minus 16 i squared end fraction equals fraction numerator 3 minus 4 i over denominator 9 plus 16 end fraction

space
space space space space space space space space space space space equals space space space space fraction numerator 3 minus 4 straight i over denominator 25 end fraction equals 3 over 25 minus 4 over 25 straight i
           = a + ib, where space space space space space space space space space straight a space equals 3 over 25 comma space space straight b space equals fraction numerator negative 4 over denominator 25 end fraction

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