Question

Find the square root of (5 + 12 i)​

Answer 1

Answer:

8.24621125

Step-by-step explanation:

at first,

2 √(5+12)

=2 √ 17

=8.24621125

Answer 2

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.

Step-by-step explanation:

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