Question

Q.2 Find square root of 4+6√-5​

Answer 1

Step-by-step explanation:

We can find the square root as follows:

Let z = 4 +6−5‾‾‾√ = 4 + 65‾√iRe(z) = 4 and Im(z) = 65‾√Now, ∣∣z∣∣ = 42 + (65‾√)2‾‾‾‾‾‾‾‾‾‾‾‾‾√ = 16 + 180‾‾‾‾‾‾‾‾‾‾√ = 14Now, z√ = ±[∣∣z∣∣ + Re(z)2‾‾‾‾‾‾‾‾√ + i∣∣z∣∣ − Re(z)2‾‾‾‾‾‾‾‾√ ] , when Im(z) > 0⇒4 + 65‾√i‾‾‾‾‾‾‾‾‾‾√ = ±[14+42‾‾‾‾‾√ + i14−42‾‾‾‾‾√ ]⇒4 + 65‾√i‾‾‾‾‾‾‾‾‾‾√ = ±(3 + 5‾√i)

Regard.