Stepwise problems - Thu. 11:59pm
Complex algebra
01
Complex arithmetic
Write each of these expressions in the form
. (a)
(b)
02
Complex solutions of quadratic equations
Find all solutions and write them in the form
.
Complex exponential
03
Complex forms - exponential to Cartesian
Write each number in the form
. (a)
(b)
04
Polar and exponential form
Write down Euler’s Formula.
Now write
: (i) in polar form
(ii) in exponential form
Complex roots
05
Complex roots using polar
Find the three cube (
) roots of . Write your answer in the form
.
Regular problems - Sat. 11:59pm
Complex algebra
06
Complex arithmetic
Write each of these expressions in the form
. (a)
(b)
07
Complex solutions of quadratic equations
Find all solutions and write them in the form
. (a)
(b)
Complex exponential
08
Polar and exponential form
Write down Euler’s Formula.
Now write each of the following complex numbers (i) in polar form, and (ii) in exponential form.
(a)
(b)
09
Complex products and quotients using polar
For each pair of complex numbers
and , compute: (a)
(b)
(Use polar forms with
.)
10
Complex powers using polar
Using De Moivre’s Theorem, write each number in the form
. (a)
(b) (First convert to polar/exponential, then compute the power, then convert back.)
Complex roots
11
Complex roots using polar
Find each of the indicated roots.
(a) The four
roots of . (b) The three cube (
) roots of . Try to write your answer in
form if that is not hard, otherwise leave it in polar form.