### Chapter 15 - Algebra Coach Exercises

**Algebra Coach Exercise on complex numbers.**

For each question perform the indicated operations.
To do this drag-and-drop each question into the
Algebra Coach and click the Simplify button repeatedly.

(Required Options settings: the *complex numbers* option must be turned on,
with *i* as the imaginary unit; and the *exact or floating point*
option must be set to *keep exact*.)
- -5 i (5 i - 6)
- 2 (5 i + 6)
- (3 i + 4) (5 i - 6)
- (3 i + 4) / (5 i + 6)
- (3 i + 4) / (-2 i)
- (3 i - 4) (3 i + 4)
- 5 / (3 i + 4)

**Algebra Coach Exercise on
complex numbers in exponential form.**

For each question perform the indicated operations.
To do this drag-and-drop each question into the
Algebra Coach and click the Simplify button repeatedly.

(Required Options settings: *complex numbers* turned on,
with *i* as the imaginary unit; *e* set to represent the
number 2.718… ; *p* set to represent the
number π ; angular measure set to radians)
- 6 e^(1.2 i)
- (6 e^(1.2 i)) * (2.2 e^(-0.4 i))
- (6 e^(1.2 i)) / (2.2 e^(-0.9 i))
- e^(i p)
- (e^(i p)) ^ 3
- (sqrt (2) e^(i p / 2)) ^ 4