Question

find the square root of √-8-6i​

Answer 1

Step-by-step explanation:

Let the square root be x+iy

⇒(x+iy)=

−8−6i

Taking square on both the side

⇒x

2

−y

2

+2xyi=−8−6i

By comparing we get.

⇒x

2

−y

2

=8 and 2xy=−6

⇒xy=−3

⇒y=

x

−3

⇒x

2

−(

x

−3

)

2

=−8

⇒x

2

−

x

2

9

=−8

⇒x

4

−9=−8x

2

⇒x

4

+8x

2

−9=0

⇒x

4

+9x

2

−x

2

−9=0

⇒x

2

(x

2

−1)+9(x

2

−1)=0

⇒(x

2

+9)(x

2

−1)=0

⇒x

2

=−9;x

2

=1

Since x is real we get x=±1

Taking x=±1 we get y=−3

⇒ square root is 1−3i

Taking x=−1 we get y=3

⇒ square root is −1+3i

Square root is ±(1−3i)