Question

Solve these complex number ques.

√4×√-3=?
√-4×√-3=?​

Answer 1

ANSWER:

To Solve:

• √4 × √-3
• √-4 × √-3

Solution:

1. √4 × √-3

We have,

$\implies \sqrt{4}\times\sqrt{-3}$

We can rewrite the above expression as,

$\implies 2\times\sqrt{(3)(-1)}$

So,

$\implies2\times\sqrt{3}\times\sqrt{-1}$

$\implies2\sqrt{3}\times\sqrt{-1}$

We know that,

$\hookrightarrow \sqrt{-1}=i$

So,

$\implies2\sqrt{3}\times\sqrt{-1}$

$\implies2\sqrt{3}i$

Therefore,

$\bf\implies \sqrt{4}\times\sqrt{-3}=2\sqrt3i$

2. √-4 × √-3

We have,

$\implies \sqrt{-4}\times\sqrt{-3}$

We can rewrite the above expression as,

$\implies \sqrt{(4)(-1)}\times\sqrt{(3)(-1)}$

So,

$\implies\sqrt{4}\times\sqrt{-1}\times\sqrt{3}\times\sqrt{-1}$

$\implies2\times\sqrt{3}\times(\sqrt{-1})^2$

$\implies2\sqrt{3}\times(\sqrt{-1})^2$

Hence,

$\implies2\sqrt3\times(-1)$

$\implies-2\sqrt3$

Therefore,

$\bf\implies \sqrt{-4}\times\sqrt{-3}=-2\sqrt3$