Question

5(4+3i)^x+(1-i)^4=5^x
solution

Answer 1

Like the last problem, write everything out in polar form first and then things will become much easier.

For example, the first expression on the LHS

5(4 + 3i)^x = 5.(5exp(alpha.i))^x = 5^(x+1).exp(x.alpha.i)
where alpha = arctan(3/4)

Answer 2

can't wait to see this

Answer 3

Then note that the RHS is real, so the LHS must be as well.

So once you've found one expression for the LHS, set the imaginary component to zero.

Answer 4

hmmm

Answer 5

no first step is
\[5\times 5e^{i\alpha x}-5^x=4\]

Answer 6

you can see that sin(alpha.x) = 0, and that gives you a big leg up.

Answer 7

second is
\[5^{x+1}e^{i \alpha x}-5^x=4\]?