If $i^{2}$ $= - 1$ , then find the value of $(2 - 3 i)^{2}$ .

- 5 - 12 i

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

4 + 6 i

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

4 + 12 i

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

5 + 12 i

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

13 - 6 i

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

Open in App

Solution

The correct option is A $- 5 - 12 i$
We know that ${(a - b)}^{2} = a^{2} + b^{2} - 2 a b$ So
${(2 - 3 i)}^{2} = 2^{2} + {(3 i)}^{2} - 2 \times 2 \times 3 i = 4 + 9 i^{2} - 12 i$
And $i$ is an imaginary number whose value is $\sqrt{- 1}$
So, $i^{2} = - 1$
$\Rightarrow 4 + 9 i^{2} - 6 i = 4 - 9 - 12 i = - 5 - 12 i$
$\Rightarrow {(2 - 3 i)}^{2} = - 5 - 12 i$

Suggest Corrections

Similar questions

\frac{\sqrt{5 + 12 i} + \sqrt{5 - 12 i}}{\sqrt{5 + 12 i} - \sqrt{5 - 12 i}} = a + i b, b < 0

a - 2 b

\sqrt{5 - 12 i} + \sqrt{- 5 - 12 i} = z

arg z

\frac{\sqrt{5 + 12 i} + \sqrt{5 - 12 i}}{\sqrt{5 + 12 i} - \sqrt{5 - 12 i}} = a + i b, b < 0

a - 2 b

$\frac{\sqrt{5 + 12 i} + \sqrt{5 - 12 i}}{\sqrt{5 + 12 i} - \sqrt{5 - 12 i}} =$

\frac{\sqrt{(5 + 12 i)} + \sqrt{(5 - 12 i)}}{\sqrt{(5 + 12 i)} - \sqrt{(5 - 12 i)}}

Join BYJU'S Learning Program