Question

find square root of 3 + 2√10i​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

To Find:

$\sqrt{3} + 2\sqrt{10}i$

Solution:

  √3 + 2√10i = a+ bi

Now, squaring on both the sides

= a² + b²i²+ 2abi    (i² = -1)

= 3+ 2√10i = (a²-b²)+ 2abi

= a² - b² = 3  and 2ab = 2√10

                                  a = $\frac{\sqrt{10} }{b}$

        $\frac{\sqrt{10} }{b})$² - b² = 3

      $\frac{10}{b^{2} }$ - b² = 3

       Multiplying the whole equation by b²

10- $b^{4}$ = 3b²

$b^{4}$ + 3b²-10 = 0

Let b² be m

m²+ 3m-10=0

m² +5m-2m-10 = 0

m(m+5)-2(m+5) = 0

(m = 2) or (m = 5) = 0

m = -2 or m = -5

Since b² = m

b = ±√2

a = ±√5

Therefore, the square root of 3+ 2√10i = ±(√5 - √2).