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Please simplify these and explain thoroughly what you did. The problems are in the picture attached. I believe them to be complex numbers. Thank you for your help and time.

Please simplify these and explain thoroughly what you did The problems are in the picture attached I believe them to be complex numbers Thank you for your help class=

Respuesta :

Answer:

[tex]5i\sqrt{3}[/tex]

- i

i

Step-by-step explanation:

1

[tex]\sqrt{-75}[/tex]

take out i which is ([tex]\sqrt{-1}[/tex]):

[tex]\sqrt{75} *\sqrt{-1} = i\sqrt{75}[/tex]

[tex]\sqrt{75} = \sqrt{5*5*3} = 5\sqrt{3}[/tex]

[tex]i\sqrt{75} = 5i\sqrt{3}[/tex]

2

[tex]i^{7} = i^{4} * i^{3} = 1* -i = -i\\\\i^{3} = i^{2} * i = -1 * i = -i[/tex]

(this above, was just a quick explanation on how i^3 is -i)

3

[tex]i^{49} = i[/tex]

lets use the reference of [tex]i^{4} = 1[/tex] :

49/4= 12 remainder 1

Using above knowledge

[tex]i^{49}[/tex] =

[tex](i^{4})^{12} * i^{1}[/tex]

(1)12 × i =

1 × i =

i

mohammedmutasim26

Answer:

1\ 8.66i

2\ -i

Step-by-step explanation:

1\

[tex] \sqrt{ - 75 } = \sqrt{75} \times \sqrt{ - 1} \\ and \sqrt{ - 1} = i \\ = 8.66i[/tex]

2\

[tex] {i}^{7} = {i}^{6} \times i \\ = {i}^{2 } \times i ^{4} \times i \\ = - 1 \times { - 1}^{2} \times i \\ = - 1 \times 1 \times i \\ = - i[/tex]

3\

Using the same steps..

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