Difference between revisions of "HW1.3 Sangwan Han - Def of Complex Number and example ECE301Fall2008mboutin" - Rhea

Revision as of 10:36, 4 September 2008

complex number combined sum of a real number and an imaginary number. the basic expression of complex number is a + bi.(a and b are real numbers) An imaginary number is a multiple of i, it mean i is $ \sqrt-1 $.

for example of complex number. calculate this. $ (4+3\sqrt2i)-(2-\sqrt2i) $

answer:

       $ = 4+3\sqrt2i - 2+\sqrt2i $
       $ = (4-2) + (3\sqrt2 + \sqrt2)i $
       $ =2 + 4\sqrt2i $

another example,

change to $ a+bi $ form.

$ ((1+i)/(1-i))^4 $

answer:

         $ =\left(\frac{\left(1+i\right)^2}{\left(1-i\right)\times\left(1+i\right)}\right)^4 $
       
          $ =((1+2i+(i)^2)/(i^2-(i)^2))^4 $
       
          $ =((1+2i-1)/(1-(-1)))^4 $
       
          $ =(2i/2)^4 $
       
          $ =i^4 $
       
          $ =((i)^2)^2 $
       
          $ =(-1)^2=1 $
       
          $ =1 + 0i $