Question

√(-5+12i) как решить?

Answer 1

Если корень под всем примером, и тебе нужно найти "i"

То решение такое: 1) возводим все в квадрат и корень исчезает

-5+12i=0

12i=5

i=5\12

Answer 2

To find the square root of a complex number, √(-5+12i), we can follow these steps:

Step 1: Write the complex number in the form a + bi. Step 2: Identify the values of a and b. Step 3: Use the formula for the square root of a complex number.

The given complex number is: -5 + 12i

Step 1: Write the complex number in the form a + bi. Here, a = -5 and b = 12.

Step 2: Use the formula for the square root of a complex number. The square root of a complex number of the form z = a + bi is given by:

√z = ±√((√(a^2 + b^2) + a) / 2) + sign(b) * √((√(a^2 + b^2) - a) / 2)i

where:

• √ is the square root,
• sign(b) returns -1 if b < 0, and 1 if b ≥ 0.

Step 3: Calculate the square root.

√((-5) + 12i) = ±√((√((-5)^2 + 12^2) + (-5)) / 2) + sign(12) * √((√((-5)^2 + 12^2) - (-5)) / 2)i

Now, let's compute the values:

√((-5)^2 + 12^2) = √(25 + 144) = √169 = 13

So, the square root becomes:

√(-5 + 12i) = ±√((13 + (-5)) / 2) + sign(12) * √((13 - (-5)) / 2)i = ±√(8 / 2) + √(18 / 2)i = ±√4 + √9i = ±2 + 3i

Therefore, the square roots of -5 + 12i are ±2 + 3i.