Question

Find the square root of : 1 + 4V3 i
​

Answer 1

Answer:

± (2 + √3i )

Step-by-step explanation:

let z²  = 1 + 4√3i =  7( 1/7 + 4√3i/7) =  7( cos2∝ + isin2∝)

cos2∝ = 1/7 = 1 - 2sin²∝

cos∝ = 2/√7 , sin∝ = √3/√7

then

z = ±√7 ( cos∝ + isin∝)  = ±√7 (2/√7 + √3i/√7)  = ± (2 + √3i )