If $a, b, c, d ϵ R$ are such that $a^{2} + b^{2} = 4$ and $c^{2} + d^{2} = 2$ and if $| a + i b |^{2} = | c + i d |^{2} | x + i y |$ then $x^{2} + y^{2} =$

4

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

3

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

2

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

1

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

Open in App

Solution

The correct option is B $4$
$| a + i b |^{2} = | c + i d |^{2} | x + i y |$
$\Rightarrow [\sqrt{a^{2} + b^{2}}]^{2} = [\sqrt{c^{2} + d^{2}}]^{2} \sqrt{x^{2} + y^{2}}$
$\Rightarrow [a^{2} + b^{2}] = 2 \sqrt{x^{2} + y^{2}}$
$x^{2} + y^{2} = 4$

Suggest Corrections

Similar questions

\in

a^{2} + b^{2} = 4

c^{2} + d^{2} = 2

(a + i b)^{2} = (c + i d)^{2} (x + i y)

x^{2} + y^{2} =

\frac{(a + i b)}{(c + i d)} = x + i y

\frac{a - i b}{c - i d} = x - i y

\frac{a^{2} + b^{2}}{c^{2} + d^{2}} = x^{2} + y^{2}

x - i y = \frac{a - i b}{c - i d}

x^{2} + y^{2} = \frac{a^{2} + b^{2}}{c^{2} + d^{2}}

x + i y = \sqrt{\frac{a + i b}{c + i d}}

(x^{2} + y^{2})^{2} = \frac{a^{2} + b^{2}}{c^{2} + d^{2}}

(x + i y) = \sqrt{\frac{a + i b}{c + i d}}

(x^{2} + y^{2})^{2} = \frac{a^{2} + b^{2}}{c^{2} + d^{2}}

Join BYJU'S Learning Program