Question

find the square root of the complex number 3i​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Concept:

To find:

Find the square root of the complex number $3i$.

Solution:

Let $a,b$ be 2 real numbers.

$\sqrt{3i} = a+ib\\3i=(a+ib)^{2} \\3i=a^2+b^2+2iab$

Separate the real and imaginary part from the abouve equation.

$a^2+b^2=0$   .......(1)

$2iab=3i$      .......(2)

$a=\frac{3}{b}$

Put the value of $a$ in equation (1).

$(\frac{3}{b} )^{2} +b^2=0\\\frac{9}{b^2}+b^2=0\\ 9+b^4=0\\b=\sqrt[4]{9}$

$a=\frac{3}{\sqrt[4]{9} }$

$\sqrt{3i}=\frac{3}{\sqrt[4]{9} }+i\sqrt[4]{9}$

Hence, we got our answer.

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