Find the real value of 'a' for which 3i³- 2ai²+(1-a)i + 5 is real.

4

(a)

If f(z) = \(\frac { 7-z }{ 1-{ z }^{ 2 } } \) where z= 1 + 2i , then find \(|f(z)|\)

4

(a)

If \(\frac { z-1 }{ z+1 } \)  is a purely imaginary number \((z\neq -1)\) then find the value of \(|z|\)

4

(a)

Find \(​​\left| (1+i)\frac { (2+i) }{ (3+i) } \right| \)

4

(a)

Find the value of \({ 2x }^{ 4 }+{ 5x }^{ 3 }+{ 7x }^{ 2 }-x+41,when\ x=-2-\sqrt { 3i } \)

4

(a)