1.

(i) If |z-3i lt sqrt5 then prove that the complex number z also satisfies the Inequality|i(z+1)+1 | lt 2 sqrt5. (ii) Find the complex number z which satisfies the condition |z-a + ai|=1 and has thegreatest absolute value where a is a real constant (a ne 0).

Answer»


Answer :`|z|_("max") = (SQRT(a^2 + 4)+a)/(2), z= PM((sqrt(a^2 + 4) +a)/(2)) i and |z|_("min") = (sqrt(a^2 + 4)-a)/(2) , z= pm ((sqrt(a^2 + 4)-a)/(2))i`, this is true for all real `a GE 0; z = pm 2I`


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