complex numbers in rectangular form

Question

You are given four complex numbers in rectangular form: p=5+3j. q=2-4j. r=6j. s=-3-2j.

Simplify the expressions below giving the answer in rectangular form:

(i) p+s
(ii) p+q
(iii) r s
(iv) r(p-q)
(v) p/q
(vi) s/r

Answer 1

p=5+3j   q=2-4j   r=6j   s=-3-2j

 

(i)  p+s = 5+3j + -3-2j = (5-3) + (3j-2j) = 2 + j    [Add real parts, add imaginary parts]

 

(ii)  You do this one just like above

 

(iii)  rs = (6j)(-3-2j) = -18j - 12j² = 12 - 18j         [FOIL it out, remember that j² = -1]

 

(iv) Do the p-q first, then multiply by r

 

(v) p/q = (5+3j)/(2-4j)

     Multiply top and bottom by the conjugate of the denominator 2+4j:

     (5+3j)/(2-4j) * (2+4j)/(2+4j)

     (10-20j+6j-12j²)/(4-16j²)

     (22-14j)/20                           [j² = -1]

 

(vi) You do this one like (v) above.  The conjugate of 6j is -6j.