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Need help figuring out if the following is Real or Complex Question number 10

Need help figuring out if the following is Real or Complex Question number 10-example-1

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Step-by-step explanation:

We have the expression:


i^3

where i represents the complex number i defined as follows:


i=√(-1)

To find if i^3 is real or complex, we represent it as follows:


i^3=i^2* i

And we find the value of i^2 using the definition of i:


i^2=(√(-1))^2

Since the square root and the power of 2 cancel each other


\imaginaryI^2=-1

And therefore, using this value for i^2, we can now write i^3 as follows:


\begin{gathered} \imaginaryI^3=\imaginaryI^2*\imaginaryI \\ \downarrow \\ \imaginaryI^3=(-1)*\imaginaryI \end{gathered}

This simplifies to -i


\imaginaryI^3=-\imaginaryI^

Because -i is still a complex number, that means that i^3 is a complex number.

Answer: Complex

User Matt Palmerlee
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