How do I write this complex number in standard form?

Question

fanduekisses · Answer

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mathmale · Answer

Hello, Fandue/Fondue,
Are you able to explain what "standard form" means here?  If not, I urge you to look through your textbook (in the section on complex numbers) for examples of "standard form."

If we cannot eliminate that imaginary operator, i, completely, we could at least write the final result in what I think is "standard form:"   (real part) + i(imag. part).

I note right away that we can make the work of expanding this 4th order expression by factoring the expression within parentheses:

$$(\frac{ \sqrt{2} }{ 2 }+\frac{ \sqrt{2} }{ 2 }i) = ( [\frac{ \sqrt{2} }{ 2 }]*[1+i])^{4}$$

mathmale · Answer

Can you now evaluate $$[\frac{ \sqrt{2} }{ 2 }^{}]^{4} ?$$
Once you have that result, you'll need to expand the binomial [1+i]^4.

mathmale · Answer

See what you can do from this point, first, and then I'll come back later, if necessary, to help you complete the solution of this problem.

mathmale · Answer

Note:$$(a+b)^4 = [(a+b)^{2}]^{2}$$

mathmale · Answer

So, how would you expand (1+i)^4?

Important:  be sure you understand what " i " represents before you start, as well as the values of $$i,i ^{2},i ^{3},i ^{4}$$