Clearing i on an equation

Question

I'm having an issue clearing i on this equation, I've tried online step by step problem solvers but for some reason they give false as if there is no solution

This is how i write the equation on those sites to clear "i", any suggestion?

$$98000=2350 \times \frac{(1+i)^{40}-1}{(1+i)^{40}i}$$

Answer 1

I would suggest you compute $(1+i)^2$, and then you should be able to compute $(1+i)^{40}$ fairly easily.

Answer 2

$(1+i)^2 = 1+2i-1 = 2i$

$(1+i)^4 = ((1+i)^2)^2 =(2i)^2=-4$

$(1+i)^{40}=((1+i)^{4})^{10}=(-4)^{10}=2^{20}$

$$\frac{(1+i)^{40}-1}{(1+i)^{40}i}=\frac{1}{i}-\frac{1}{(1+i)^{40}i}$$

Substituting $(1+i)^{40}=2^{20}$ and $1/i=-i$

$$\implies-i+i(2^{-40})$$

$$\implies i(2^{-40}-1)$$

This is a pure imaginary number. Your equation in the question is wrong.