Multiplication of complex exponential numbers

• Jan 17th 2008, 10:21 PM
OzzMan
Multiplication of complex exponential numbers
(625e^(3.46i))*(4.4e^(1.22i))

when i multiply it out i get 2750e^(4.2212i) From there I'm supposed to make it into polar and rectangular forms. the answers in the book are 2750(cos268.1 degrees + i*sin268.1 degrees) for polar form and -89.1 -2750i for rectangular form. Both my answers were incorrect according to the book. So my multiplication must have been off, if anyone can check it for me please.
• Jan 17th 2008, 11:00 PM
CaptainBlack
Quote:

Originally Posted by OzzMan
(625e^(3.46i))*(4.4e^(1.22i))

when i multiply it out i get 2750e^(4.2212i) From there I'm supposed to make it into polar and rectangular forms. the answers in the book are 2750(cos268.1 degrees + i*sin268.1 degrees) for polar form and -89.1 -2750i for rectangular form. Both my answers were incorrect according to the book. So my multiplication must have been off, if anyone can check it for me please.

First $\displaystyle 3.46+1.22=4.68$ not $\displaystyle 4.22$, so you should have: $\displaystyle 2750 e^{4.22i}$ since:

$\displaystyle (625e^{3.46i})\times (4.4e^{1.22i})=625 \times 4.4 \times e^{(3.46+1.22)i}$

and $\displaystyle 4.46$ radian is $\displaystyle 268.1$ degrees (rounded to that precission).

Of course you should also know that:

$\displaystyle e^{i \theta}=\cos(\theta)+i \sin(\theta)$

RonL
• Jan 17th 2008, 11:18 PM
OzzMan
woops i multiplied exponents.