If $(2 + i) (2 + 2 i) (2 + 3 i) . . . . . . . (2 + n i) = x + i y$ , then $5.8.13..... (4 + n^{2}) =$

x^{2} - y^{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x^{2} + y^{2}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

x^{4} - y^{4}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x^{4} + y^{4}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $x^{2} + y^{2}$
Given,
$(2 + i) (2 + 2 i) (2 + 3 i) . . . . . . . (2 + n i) = x + i y$ .
Now taking modulus both sides we get,
$| (2 + i) (2 + 2 i) (2 + 3 i) . . . . . . . (2 + n i) | = | x + i y |$
or, $| (2 + i) | . | (2 + 2 i) | . | (2 + 3 i) | . . . . . . . . | (2 + n i) | = | x + i y |$ [ Since $| a . b | = | a | . | b |$ for $a, b$ being complex number]
or, $5.8.13...... (4 + n^{2}) = x^{2} + y^{2}$

Suggest Corrections

Similar questions

(x^{2} - y^{2}) : (x^{2} + y^{2})

(x^{4} - y^{4}) : (x + y)^{4}

\frac{x^{4} - y^{4}}{x^{2} + y^{2}}

Divide $x^{4} - y^{4}$ by $x^{2} - y^{2}$ .

x^{4} + x^{2} y^{2} + y^{4}

Join BYJU'S Learning Program