A First Course in Complex Analysis · Problem 40

Integration — Beck, Marchesi, Pixton & Sabalka

Mathematics — Complex Analysis · complex-exponentials

Problem

Convert the following expressions to the form

x + iy

. (Reason carefully.) ((a))

e^{i\pi}

((b))

e^{\pi}

((c))

i^i

((d))

e^{\sin(i)}

((e))

\exp(\operatorname{Log}(3+4i))

((f))

(1+i)^{\frac{1}{2}}

((g))

\sqrt{3}\,(1-i)

((h))

\left(\frac{i+1}{\sqrt{2}}\right)^4