Question

find the square root of complex number -8+6i​

Answer 1

Answer:

find the square roots of 1+6i

solution

let x+iy= square root of 1+6i squaring both side

(x^2 -y^2)+i2xy=1-36+12i=-35+12i

by comparison

(x^2 -y^2)=-35 and 2xy=12 means xy=6 than y=6/x

x^2-36/x^2=-35

x^4-36/x^2=-35

x^4-36=-35x^2

X^4+35x^2-36=0 let x^2=k than x^4=k^2

k^2+35k-36=0

k^2-36k+k-36=0

(k+1)(k-36)=0

k=-1 or k=36

x^2=-1 means x=i or x^2=36 neglecting value of x=i as x is real value

x=6 or x=-6

than y=6/6 or y=6/-6

y=1 0r y=-1

square root ill be -6+i or -6-i or 6+i or 6-i

answer

6+i

6-i

-6-i

-6+i