Complex Analysis: Theory and Applications · Problem 1.2.1

Complex Numbers — Howell & Matthews

Mathematics — Complex Analysis · complex-arithmetic

Problem

Perform the required calculations and express your answers in the form

a + bi

. (a)

i^{275}

. (b)

\dfrac{1}{i^5}

. (c)

\text{Re}(i)

. (d)

\text{Im}(2)

. (e)

(i-1)^3

. (f)

(7-2i)(3i+5)

. (g)

\text{Re}(7+6i) + \text{Im}(5-4i)

. (h)

\text{Im}\!\left(\dfrac{1+2i}{3-4i}\right)

. (i)

\dfrac{(4-i)(1-3i)}{-1+2i}

. (j)

\overline{(1+i\sqrt{3})(i+\sqrt{3})}