Question

find the squre root of -15-8i​

Answer 1

Answer →

$\sqrt{ - 15 - 8i} = 4- i$

Solution→

As we know that square root of complex numbers =

$( \frac{ \sqrt{ |z| + re(z)} }{ \sqrt{2} } - i \sqrt{ \frac{ |z| - re(z)}{2} }$

Let assume that-15-8i = z

So according to the formula :-

Re (z) = -15

$|z| = \sqrt{re( {z}^{2} ) + im( {z)}^{2} }$

$|z| = \sqrt{225 + 64}$

$|z| = \sqrt{289}$

$|z| = 17$

Now putting value in formula -

$\sqrt{15 - 8i} = \sqrt{ \frac{17 + 15}{2} } - i \sqrt{ \frac{17 - 15}{2} }$

$\sqrt{ - 15 - 8i} = \sqrt{ \frac{36}{2} } - i \sqrt{ \frac{2}{2} }$

$\sqrt{ - 15 - 8i} = 4 - i$

Hope it helps