If x - a - bi is a complex number such that x2 - 3 - 4i and x3 - 2 - 11i- where i - -1- then a- b equal to

Given that x^ 2 =3+4i nbsp; nbsp; nbsp; nbsp; nbsp; ...(1)and x^ 3 =2+11i nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; ...

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Complex Numbers

If x = a + ...

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

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List I

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\begin{matrix} List I & List II (A) & Let z, ω, α be complex numbers such that & (P) & 0 | z | = | ω | = 4 and α = \frac{z - ¯ ¯ ¯ ω}{16 + z ¯ ¯ ¯ ω} . Then Re (α) is equal to (B) & If x = p + i q is a complex number such that & (Q) & 3 x^{2} = 3 + 4 i and x^{3} = 2 + 11 i, where i = \sqrt{- 1}, then p + q is equal to (C) & Number of complex number(s) z satisfying the & (R) & 4 equation ¯ ¯ ¯ z = i z^{2}, where i = \sqrt{- 1}, is equal to (D) & If z \in C satisfies | z + 2 - i | = 5, then the & (S) & 5 maximum value of \frac{| 3 z + 9 - 7 i |}{4} is equal to \end{matrix}

List I

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\begin{matrix} List I & List II (A) & Let z, ω, α be complex numbers such that & (P) & 0 | z | = | ω | = 4 and α = \frac{z - ¯ ¯ ¯ ω}{16 + z ¯ ¯ ¯ ω} . Then Re (α) is equal to (B) & If x = p + i q is a complex number such that & (Q) & 3 x^{2} = 3 + 4 i and x^{3} = 2 + 11 i, where i = \sqrt{- 1}, then p + q is equal to (C) & Number of complex number(s) z satisfying the & (R) & 4 equation ¯ ¯ ¯ z = i z^{2}, where i = \sqrt{- 1}, is equal to (D) & If z \in C satisfies | z + 2 - i | = 5, then the & (S) & 5 maximum value of \frac{| 3 z + 9 - 7 i |}{4} is equal to \end{matrix}

z = 3 + 4 i

x^{3} - x^{2} + x + 46

x = 2 + 3 i

a

b

(2 + α)^{4} = a + b α

α = \frac{- 1 + i \sqrt{3}}{2},

a + b

| z | + z = 3 + i

i

\sqrt{- 1)} .

| z |

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