Let `z in C` be such that `|z| lt 1 `.If `omega =(5+3z)/(5(1-z)` thenA. `4 Im ( omega) gt 5`B. `5 Re (omega) gt 1`C. `5 Im(omega) lt 1 `D.

Let `z in C` be such that `|z| lt 1 `.If `omega =(5+3z)/(5(1-z)` thenA

1.	Let `z in C` be such that `\|z\| lt 1 `.If `omega =(5+3z)/(5(1-z)` thenA. `4 Im ( omega) gt 5`B. `5 Re (omega) gt 1`C. `5 Im(omega) lt 1 `D.
Answer» Correct Answer - B Given complex number `omega=(5+3z)/(5(1-z))` `rArr 5 omega -5 omega z=5+3z` `rarr (3+5 omega)z=5 omega-5` `rArr \|3+5 omega\|\|z\|=\|5 omega- 5\|` [applying modulus both sides and `\|z_1z_2\|=\|z_2\|\|z_2\|]` `therefore \| z\| lt 1 ` `therefore \|3+5 omega\| gt \|5 omega - 5\|" "["from Eq.(i)"]` `rArr " "\|omega+3/5\| gt \| omega-1\|` Let `omega` =x+iy, then `(x+3/5)^2+y^2 gt (x-1)^2+y^2` `rArr x^2+9/25+6/5 x lt x^2 +1 -2x` `rArr 16x/5 gt 16/25 rArr x gt 1/5 rArr lt 1` `rArr 5 Re(omega ) gt 1`

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Let `z in C` be such that `|z| lt 1 `.If `omega =(5+3z)/(5(1-z)` thenA. `4 Im ( omega) gt 5`B. `5 Re (omega) gt 1`C. `5 Im(omega) lt 1 `D.

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