First slide

Algebra of complex numbers

Question

${if x=a+ib is a complx number such that x}^{2} = 3 + 4 i and x^{3} = 2 + 11 i where i = \sqrt{- 1}, then (a + b) equals to$

Moderate

Solution

$x = \frac{x^{3}}{x^{2}} = \frac{2 + 11 i}{3 + 4 i} \times \frac{3 - 4 i}{3 - 4 i} = \frac{50 + 25 i}{25} = 2 + i$

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