Question

find square root of 1+4√3i​

Answer 1

Answer:

$\sqrt{1+4\sqrt{3}i}=2+\sqrt3i$

Step-by-step explanation:

Given : Expression $1+4\sqrt{3}i$

To find : The square root of the expression ?

Solution :

To find the square root of $1+4\sqrt{3}i$

We can write the expression as

$1+4\sqrt{3}i=(2)^2+(\sqrt3i)^2+2\times 2\times \sqrt3i$

The RHS form an identity, $a^2+b^2+2ab=(a+b)^2$

$1+4\sqrt{3}i=(2+ \sqrt3i)^2$

Taking root both side,

$\sqrt{1+4\sqrt{3}i}=2+\sqrt3i$

Therefore, $\sqrt{1+4\sqrt{3}i}=2+\sqrt3i$