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Complex Numbers question

2025 · 23 Jan · Shift 2 · Q46

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JEE Main
Mathematics
Complex Numbers
2025 · 23 Jan · Shift 2 · Q46

Complex Numbers question

2025 · 23 Jan · Shift 2 · Q46

JEE MainMathematicsComplex NumbersNumerical+4 / −1

Let

\alpha, \beta

be the roots of the equation

x^2-\mathrm{ax}-\mathrm{b}=0

with

\operatorname{Im}(\alpha)\lt \operatorname{Im}(\beta)

. Let

\mathrm{P}_{\mathrm{n}}=\alpha^{\mathrm{n}}-\beta^{\mathrm{n}}

. If

\mathrm{P}_3=-5 \sqrt{7} i, \mathrm{P}_4=-3 \sqrt{7} i, \mathrm{P}_5=11 \sqrt{7} i

and

\mathrm{P}_6=45 \sqrt{7} i

, then

\left|\alpha^4+\beta^4\right|

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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