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The greatest value of the modulus of the...

The greatest value of the modulus of the complex number `' z '` satisfying the equality `|z+1/z|=1` is: `(-1+sqrt(5))/2` (b) `sqrt((3+sqrt(5))/2)` `sqrt((3-sqrt(5))/2)` (d) `(sqrt(5+1))/2`

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The greatest value of the modulus of the complex number 'z' satisfying the equality |z+(1)/(z)|=1 is: (-1+sqrt(5))/(2) (b) sqrt((3+sqrt(5))/(2))sqrt((3-sqrt(5))/(2))(d)sqrt(5+1)

1/(sqrt(2)+sqrt(3)+sqrt(5))+1/(sqrt(2)+sqrt(3)-sqrt(5))

(1)/(sqrt(2)+sqrt(3)-sqrt(5))+(1)/(sqrt(2)-sqrt(3)-sqrt(5))

(1+sqrt(2))/(sqrt(5)+sqrt(3))+(1-sqrt(2))/(sqrt(5)-sqrt(3))

The complex number z which satisfy the equations |z|=1 and |(z-sqrt(2)(1+i))/(z)|=1 is: (where i=sqrt(-1) )

If |z-3i| ltsqrt5 then prove that the complex number z also satisfies the inequality |i(z+1)+1| lt2sqrt5 .

(1)/(2sqrt(5)-sqrt(3))-(2sqrt(5)+sqrt(3))/(2sqrt(5)+sqrt(3)) =

If z complex number satisfying |z-3|<=5 then range of |z+3i| is (where i= sqrt(-1) )