Question

find the square root of z=-4+i8​

Answer 1

Answer:

Let

−4−3i

=a+ib

−4−3i=a

2

−b

2

+2aib

a

2

−b

2

=−4,ab=

2

−3

ab=

2

−3

⇒b=

2a

−3

a

2

−b

2

=−4⇒a

2

−

4a

2

9

=−4

4a

4

−9=−16a

2

4a

4

+16a

2

−9=0

4a

4

+18a

2

−2a

2

−9=0

2a

2

(2a

2

+9)−1(2a

2

+9)=0

a=±

2

1

,a=±i

2

3

b=±

2

3

,b=±

2

1

Therefore,

−4−3i

=±

2

1

(1+3i)

or ±

2

1

(3+i)

Answer 2

Step-by-step explanation:

sbhgsshdhdhsgshdhehwh