Question

find the square root of 5 and 12​

Answer 1

Answer:

Suppose that a+bi is a square root of 5 +

12i.

Then, (a+bi)^2 = (a^2 - b^2) + (2ab)i = 5 + 12i.

Equate real and imaginary parts: a^2 - b^2 = 5

2ab = 12 ==> b = 6/a.

So, a^2 - (6/a)^2 = 5

==> a^2 - 36/a^2 = 5

a^4 -5a^2 - 36 = 0. › (a^2 -9)(a^2 + 4) = 0.

=> Since a must be real, a = 3 or -3. This gives b = 2 or -2, respectively.

Thus, we have two square roots: 3+2i or -3-2i.