GATE 2024 EE – Question 31
Consider the complex function $f(z)=\cos z+e^{z^2}$. The coefficient of $z^5$ in the Taylor series expansion of $f(z)$ about the origin is ______ (rounded off to 1 decimal place).
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Correct answer: -0.01 to 0.01
Explanation
$\cos z$ contains only even powers of $z$, and $e^{z^2}=\sum z^{2n}/n!$ also contains only even powers. So the coefficient of $z^5$ is 0.0.