(iii) `(1+i)/(sqrt(2))=sqrt(i)`

Prove that : (i) sqrt(i)= (1+i)/(sqrt(2)) (ii) sqrt(-i)=(1- i)/(sqrt(2)) (iii) sqrt(i)+sqrt(-i)=sqrt(2)

Express each of the following in the form (a + ib): (i)" "(i)/((1+i))" "(ii)" "(-1+sqrt(3)i)^(-1)" "(iii)" "(5+sqrt(2)i)/(1=sqrt(2)i)

Express the result in the form x+iy, where x,y are real number i=sqrt(-1) : (i) (-5+3i)(8-7i) (ii) (-sqrt(3)+sqrt(-2))(2sqrt(3)-i) (iii) (sqrt(2)-sqrt(3)i)^(2)

Express the following in the form a+ib (i) (5+sqrt(2i))/(1-sqrt(2i)) (ii)

If z=pi/4(1+i)^4((1-sqrt(pi)i)/(sqrt(pi)+i)+(sqrt(pi)-i)/(1+sqrt(pi)i)),then"((|z|)/(a m p(z))) equal

sqrt(i)+sqrt(-i)=sqrt(2)

sqrt(i)-sqrt(-i)=sqrt(2)

Express the result in the form x+iy, where x,y are real number i=sqrt(-1) : (i) (5+sqrt(2)i)/(1-sqrt(2)i) (ii) (2+i)/((1+i)(1-2i)) .

(sqrt(5+2i^(2))+sqrt(5-2i))/(sqrt(5+2i)-sqrt(5-2i))

The complex number, z=((-sqrt(3)+3i)(1-i))/((3+sqrt(3)i)(i)(sqrt(3)+sqrt(3)i))