Question

suppose three real number a,b,c are in geometric progression. let z=a+ib|/c-ib, then​

Answer 1

Answer:

Hope this helps.

I guess you need to simplify the expression for z.

Given:  b / a = c / b ,  or equivalently,  ac = b².

$\displaystyle\frac{a+ib}{c-ib} = \frac{(a+ib)(c+ib)}{(c-ib)(c+ib)}\\ \\=\frac{(ac-b^2)+(ab+bc)i}{c^2+b^2}\\ \\=\frac{(ac -ac) + b(a+c)i}{c^2+ac}\\ \\=\frac{b(a+c)i}{c(a+c)}\\\\=\bigl(\tfrac{b}{c}\bigr)i = \bigl(\tfrac{a}{b}\bigr)i$

Answer 2

Answer:

Step-by-step explanation:

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