Can somebody show me how to do this one?

[Guest]

Evaluate

3 X Re(1 + i - i ^3/i) + 2 X Im(i^4 + 3i + 4/2i)

thanks in advance

 

[Denis]

Evaluate
3 X Re(1 + i - i ^3/i) + 2 X Im(i^4 + 3i + 4/2i)

Geez americo, WHAT IS that?
Is X = multiplication sign? If so, use * instead.
What's "Re" and "Im"?

Is your expression really: 3(1 + i - i^2) + 2i(i^3 + 3) + 4/i ?

 

[pka]

If it is indeed it is \(\displaystyle 3\rm Re\nolimits (1 + i - i^2 )\) then that equals 6 because \(\displaystyle \rm Re\nolimits (1 + i - i^2 ) = \rm Re\nolimits (2 + i) = 2\) .
Re stands for real part, Re(a+ib)=a.

Moreover, \(\displaystyle \frac{1}{i} = - i\quad \Rightarrow \quad \frac{4}{{2i}} = - 2i\quad \Rightarrow \quad i^4 - 3i + \frac{4}{{2i}} = 1 - 5i\) .


\(\displaystyle \rm Im\nolimits (1 - 5i) = - 5\) , the imaginary part: Im(a+ib)=b.

 

[Guest]

thanks I will show my working next time...

I read the rules of this forum...

 

[Denis]

Soooo...Re = real part, Im = imaginary part :idea:

It's always a "good day" when you learn something new :wink: