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if z=(a+jb)/(c+jd),where a,b,c and d are real quantities?
show that; (a)if z is real then (a/b)=(c/d)
(b) if z is entirely imaginary then (a/b)=(-d/c)
1 Answer
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- Anonymous7 years ago
z = {(a + jb)(c - jd)}/{c + jd)(c - jd)} = {ac + bd + j(bc -ad}/(c² + d²).
(a) If z is real, then j(bc - ad) = 0 and bc = ad, giving a/b = c/d.
(b) If z is purely imaginary, then ac + bd = =, giving ac = - bd and
a/b = -d/c.
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