Respuesta :

Answer:

[tex]2 \sqrt{2} + i \sqrt{2} [/tex]

Step-by-step explanation:

The square of a complex number is a complex number. Here, we have:

[tex] {(a + bi)}^{2} = 6 + 8i[/tex]

[tex] {a}^{2} + 2abi - {b}^{2} = 6 + 8i[/tex]

We then have this system of equations:

[tex] {a}^{2} - {b}^{2} = 6[/tex]

[tex]2ab = 8[/tex]

Solving this system:

[tex]ab = 4[/tex]

[tex]b = \frac{4}{a} [/tex]

[tex] {a}^{2} - {( \frac{4}{a}) }^{2} = 6 [/tex]

[tex] {a}^{2} - \frac{16}{ {a}^{2} } = 6 [/tex]

[tex] {a}^{4} - 16 = 6{a}^{2} [/tex]

[tex] {a}^{4} - 6 {a}^{2} - 16 = 0[/tex]

[tex]( {a}^{2} - 8)( {a}^{2} + 2) = 0[/tex]

[tex] {a}^{2} = 8[/tex]

[tex] a = 2 \sqrt{2} [/tex]

[tex]b = \frac{4}{2 \sqrt{2} } = \sqrt{2} [/tex]

whereismybrain001

Answer: NaN

Step-by-step explanation: The square root of a complex number can be determined using a formula. Just like the square root of a natural number comes in pairs (Square root of x2 is x and -x), the square root of complex number a + ib is given by √(a + ib) = ±(x + iy), where x and y are real numbers.

http://www.math.com/students/calculators/source/square-root.htm

that's the website I used

You can also maybe do it on a scientific calculator?

Hope that's helpful

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