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Zigmanuir [339]
3 years ago
6

Complex number 5+the square root of -9

Mathematics
2 answers:
devlian [24]3 years ago
8 0
I hope this helps you


i^2= -1


5+ square root of -1.9



5+ square root of i^2.3^2


5+3i
Elden [556K]3 years ago
6 0
A raiz de -9 = a +-3 
ou seja 5+3=8
5-3=2
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Here is the answer to the equation. The photo below is the work shown.

x^2-3x-18

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Use complete sentences to describe why √-1 ≠ -√1
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Well let's say that to compare these two numbers, we have to start with the definition first.

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\displaystyle \large{ {y}^{2}  = x} \\  \displaystyle \large{ y =  \pm  \sqrt{x} }

Looks like we can use any x-values right? Nope.

The value of x only applies to any positive real numbers for one reason.

As we know, any numbers time itself will result in positive. No matter the negative or positive.

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\displaystyle \large{  {a}^{2}  = a \times a =  |b| }

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\displaystyle \large{  {2}^{2}  = 2 \times 2 = 4} \\  \displaystyle \large{  {( - 2)}^{2}  = ( - 2) \times ( - 2) =  | - 4|  = 4}

So basically, their counterpart or opposite still gives same value.

Then you may have a question, where does √-1 come from?

It comes from this equation:

\displaystyle \large{   {y}^{2}  =  - 1}

When we solve the quadratic equation in this like form, we square both sides to get rid of the square.

\displaystyle \large{   \sqrt{ {y}^{2} } =   \sqrt{ - 1}  }

Then where does plus-minus come from? It comes from one of Absolute Value propety.

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\displaystyle \large{  \sqrt{ {x}^{2}  } =  |x|  }

Solving absolute value always gives the plus-minus. Therefore...

\displaystyle \large{  y =   \pm \sqrt{ - 1}  }

Then we have the square root of -1 in negative and positive. But something is not right.

As I said, any numbers time itself of numbers squared will only result in positive. So how does the equation of y^2 = -1 make sense? Simple, it doesn't.

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Then we have another number which is -√1. This one is simple.

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So what is the different? The different between two numbers is that √-1 does not exist in a real number system since any squared numbers only result in positive while -√1 is one of the solution from y^2 = 1 and exists in a real number system.

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