Question

find the square roots of

-11 - 60√(-1)​

Answer 1

Answer:

Step-by-step explanation:

(-11-60√-1)^2

(-11-60×-1)^2

(-11+60)^2

49^2

2401

Answer 2

Answer:±(5-6i)

Step-by-step explanation:

-11-60√-1 ⇒-11-60i                         [∴i²=-1]

let square root of -11-60i be in the form of x+yi

(x+yi)² = -11-60i

x²-y²+2xyi= -11-60i

x²-y²=-11        ............(1)

2xyi= -60i ⇒xy=-30 ⇒ y = -30/x              ............(2)

put in equation 1  

x²-($\frac{-30}{x}$)²= -11

x²-900/x² = -11

x^4-900 = -11x²

x^4+11x² -900 = 0

x^4+36x² - 25x² - 900 = 0

x²(x²+36) - 25(x²+36) = 0

(x²-25)(x²+36)=0

x²=25        ; x²= -36

x = ±5        ; x=±6i

y= ±6i         ;y= ±5

answer : ±(5-6i)