If z is a complex number such that \(|z-1|=|z+1|\)  then show that Re(z) = 0.

4

(a)

Find the modulus and argument of \(z=\frac { (1+i)^{ 13 } }{ (1+i)^{ 7 } }\)

4

(a)

If (1+i)(1+2i)(1+3i)...(1+ni)=(x+iy), then show that 2.5.10....(1+n²)=x²+y²

4

(a)

Find the value of x and y, if \(\frac { \left( 1+i \right) x-2i }{ 3+i } +\frac { \left( 2-3i \right) y+i }{ 3-i } =i\)

4

(a)

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

4

(a)