Complex Numbers

adambinch

New member
Joined
Mar 8, 2008
Messages
3
Can you please help me with the following:

(1) How can I express, z = 7e^i(pie)/3 in the form of the compex number z = 4 + 3i

(2) How can I express....

x-1 / 2+j + y-1 / -1+2j
...In the form a +jb, where x, y, a and b are real.

Thanks
 
These are very difficult with your present notaion.

Do you mean 73  ei  π\displaystyle \frac{7}{3}\;e^{i\;\pi} or 7eiπ3\displaystyle 7e^{i\frac{\pi}{3}} or something else?
 
Hello, Adam!

(2) Express:   x12+j+y11+2j in the form a+bj\displaystyle \text{(2) Express: }\;\frac{x-1}{2+j} + \frac{y-1}{-1+2j}\:\text{ in the form }\,a +bj

We have:   x12+jy112j\displaystyle \text{We have: }\;\frac{x-1}{2+j} - \frac{y-1}{1-2j}

Rationalize the fractions:

. . x12+j2j2jy112j1+2j1+2j\displaystyle \frac{x-1}{2+j}\cdot\frac{2-j}{2-j} - \frac{y-1}{1-2j}\cdot\frac{1+2j}{1+2j}

. . =  (x1)(2j)4j2(y1)(1+2j)14j2\displaystyle =\;\frac{(x-1)(2-j)}{4-j^2} - \frac{(y-1)(1+2j)}{1-4j^2}

. . =  2xxj2+j4+1    y2yj12j1+4\displaystyle = \;\frac{2x - xj - 2 + j}{4+1} \;-\; \frac{y - 2yj - 1 - 2j}{1 + 4}

. . =  (2xxj2+j)(y2yj12j)5\displaystyle =\;\frac{(2x-xj - 2 + j) - (y - 2yj - 1 - 2j)}{5}

. . =  2xxj2+jy+2yj+12j5\displaystyle = \;\frac{2x - xj - 2 + j - y + 2yj + 1 - 2j}{5}

. . =  2xy1xj+2yj+3j5\displaystyle =\;\frac{2x - y - 1 - xj + 2yj + 3j}{5}

. . =  (2xy1)+(x+2y+3)j5\displaystyle = \;\frac{(2x - y - 1) + (-x + 2y + 3)j}{5}

. . =  (2xy15)a  +  (x+2y+35)bj\displaystyle =\; \underbrace{\left(\frac{2x-y-1}{5}\right)}_a \;+ \;\underbrace{\left(\frac{-x+2y+3}{5}\right)}_bj

 
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