InterviewSolution
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InterviewSolution
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If `z = 3 + 2i`, prove that `z^(2) - 6z + 13 = 0` and hence deduce that `3z^(3) - 13z^(2) + 9z + 65 = 0`. |
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Answer» `z = 3 + 2i rArr z -3 = 2i rArr (z - 3)^(2) = 4i^(2)` `rArr" "z^(2) - 6z + 13 = 0" "...(i)`. Thus, `z^(2) -6z + 13 = 0`. Now, `3z^(3) - 13z^(2) + 9z + 65 = 3z(z^(2) - 6z + 13)+5(z^(2) - 6z + 13)=(3z xx 0) + (5 xx 0) = 0" "["using (i)"]` Hence, `3z^(2) - 13z^(2) + 9z + 65 = 0`. |
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