Find the square roots of $3 - 4 i$ .

(2 - i)

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

(3 - i)

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

(- 2 + i)

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

(- 3 + i)

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

Open in App

Solution

The correct options are
B $(2 - i)$
D $(- 2 + i)$
Let the square root $3 - 4 i$ be $a + i b$

$\Rightarrow (3 - 4 i) = (a + i b)^{2}$

$\Rightarrow 3 - 4 i = a^{2} - b^{2} + i (2 a b)$

Comparing both sides ;

$\Rightarrow 3 = a^{2} - b^{2}$ and $2 a b = - 4$

Solving above two equations, we obtain

$a = 2, b = - 1$ or $a = - 2, b = 1$

$∴$ Square root of $3 - 4 i$ is : $(2 - i)$ or $(- 2 + i)$

Suggest Corrections

Similar questions

3 + 4 i

- 5 + 12 i

3 + 4 i

i = \sqrt{- 1}

2 + 2 \sqrt{3} i

1 + 4 \sqrt{3 i}

3 + 2 \sqrt{10} i

2 (1 - \sqrt{3} i)

\frac{(1 + i) (2 + 3 i) (3 - 4 i)}{(2 - 3 i) (1 - i) (3 + 4 i)} = a + i b

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

Join BYJU'S Learning Program