Unable to simplify exponential expression to its simplest form of trigonometric expression by Euler's formula

Applying "FullSimplify" fails to simplify the following expressions:

Input:

FullSimplify[(-0.0001+0.01*I)*E^((-1.6*10^7-2.1*10^8*I)*t)-(0.0001+0.01*I)*E^((-1.6*10^7+2.1*10^8*I)*t)]

Output:

(-0.0001 + 0.01 I) E^((-1.6*10^7 - 2.1*10^8 I) t) - (0.0001 + 0.01 I) E^((-1.6*10^7 + 2.1*10^8 I) t)

However, in fact, by applying Euler's formula, the above expression can be manually simplified to:

-2*(0.0001*Cos[-2.1*10^8*t] + 0.01*Sin[-2.1*10^8*t])*E^(-1.6*10^7*t)

How can I do to simplify to this form in Mathematica？

Thank you very much!

• Have you already seen ExpToTrig[]? Commented Jun 10, 2022 at 15:52
• ExpToTrig[] makes the expression more complex. The output is: (-0.0001 - 0.01 I) Cos[(2.1*10^8 + 1.6*10^7 I) t] - (0.0001 - 0.01 I) Cosh[(1.6*10^7 + 2.1*10^8 I) t] + (0.01 - 0.0001 I) Sin[(2.1*10^8 + 1.6*10^7 I) t] + (0.0001 - 0.01 I) Sinh[(1.6*10^7 + 2.1*10^8 I) t]. Moreover, the terms of Sinh[] and Cosh[] cannot be cancelled out with TrigExpand[] or TrigReduce[]. Commented Jun 10, 2022 at 15:59

expr = (-0.0001 + 0.01*I)*

$$-0.0002 e^{-1.6\times 10^7 t} (1. \cos (2.1\times 10^8 t)-100. \sin (2.1\times 10^8 t))$$