Question

what is square root of -16+30i​

Answer 1

Answer:

+or-(3+5i)

Step-by-step explanation:

Let square root of -16+30i be x+yi

(-16+30i)^1/2=x+yi

On squaring both the sides we get

-16+30i=x^2-y^2+2xyi

On comparing both the sides

2xy=30

x=15/y........1

-16=x^2-y^2------------------2

Substitute the value of x in Eqn 2 we get

-16y^2=225-y^4

y^4-16y^2-225=0

y^4-25y^2+9y^2-225=0

y^2(y^2-25)+9(y^2-25)=0

(y^2-25)(y^2+9)=0

y=+5 or -5

y can't be 3i

square root =when y=5 =》x=15/5=3

when y=-5=》x=-3

square root =》3+5i or -3-5i