150000 = 45000*[(1+i)^5-1]/[i*(1+i)^5] +12000/(1+i)^5
You asked:
Solve the equation \(150000 = \frac{45000 \left({\left( 1 + i \right)}^{5} - 1\right)}{i {\left( 1 + i \right)}^{5}} + \frac{12000}{{\left( 1 + i \right)}^{5}}\) for the variable \(i\).
MathBot Answer:
This equation has no unknown quantities, so it is either true or false.
This equation is false because the left-hand side is not equal to the right-hand side.
The left-hand side of the equation is:
\[150000\]The right-hand side of the equation is:
\[\frac{45000 \left({\left( 1 + i \right)}^{5} - 1\right)}{i {\left( 1 + i \right)}^{5}} + \frac{12000}{{\left( 1 + i \right)}^{5}} = - \frac{45000 i \left(-1 + \left(1 + i\right)^{5}\right)}{\left(1 + i\right)^{5}} + \frac{12000}{\left(1 + i\right)^{5}}\]\(i\) is the imaginary unit, defined as \(i^2 = -1\).