if $$x=a+ib$$ is a complx number such that $$x2=3+4i$$ and $$x3=2+11i$$ where $$i=-1$$,then $$a+b$$ equals to

$$x=x3x2=2+11i3+4i$$×$$3-4i3-4i=50+25i25=2+i$$

Algebra of complex numbers

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Question

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

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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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