Find the value of $(4 + 2 i) (4 - 2 i)$ given that $i^{2} = - 1$ .

12

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

20

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

16 - 4 i

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

4 + 16 i

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

12 - 16 i

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

Open in App

Solution

The correct option is B $20$
After expanding, we get $(4 + 2 i) (4 - 2 i) = 16 + 8 i - 8 i - 4 i^{4}$
According to the question $i^{2} = - 1$
$\Rightarrow 16 - 4 i^{4}$
$\Rightarrow 16 - 4 (- 1)$
$\Rightarrow 16 + 4 = 20$

Suggest Corrections

Similar questions

{sin}^{2} \frac{π}{16} + {sin}^{2} \frac{3 π}{16} + {sin}^{2} \frac{5 π}{16} + {sin}^{2} \frac{7 π}{16}

(2 ¯ i + 4 ¯ j + 2 ¯ ¯ ¯ k) \times (2 ¯ i - x ¯ j + 5 ¯ ¯ ¯ k) = 16 ¯ i - 6 ¯ j + 2 x ¯ ¯ ¯ k

x

I^{2} - 16 I + 64

Show that one and only one out of n, n + 4,n+8, n + 12, and n + 16

Is divisible by 5 Where n is any positive integer

Join BYJU'S Learning Program