Simplify: `(5+3i)/(1+2i)+(3+7i)/(1-2i)`

Simplify : (1+2i)/(1-2i)-(1-2i)/(1+2i)

Express the result in the form x+iy, where x,y are real number i=sqrt(-1) : (i) (5+9i)-:(-3+4i) (ii) [(sqrt(5)+(i)/(2))(sqrt(5)-2i)]-:(6+5i) (iii) ((1-i)(2-i)(3-i))/(1+i) (iv) (1+3i)/((1-2i)^(2))

Simplify : (i)" "(-2i)((1)/(6)i)" "(ii)" "(-i)(3i)((-1)/(6)i)^(3)" "(iii)" "4 sqrt(-4)+5 sqrt(-9)-3 sqrt(-16)

1 Simplify: (i) 2^((2)/(3)) times 2^((1)/(5) and ((1)/(3)^(3))^(7)

Simplify ( i ) (((1)/(3))^(-2)-((1)/(2))^(-3)}-:((1)/(4))^(-2)*( ii) ((5)/(8))^(-7)xx((8)/(5))^(-5)

Simplify (i) 2^(2/3). 2^(1/3) (ii) (3^(1/5))^4 (iii) (7^(1/5))/(7^(1/3)) (iv) 13^(1/5). 17^(1/5)

Simplify : (i) 2^(2/3). 2^(1/5) (ii) (1/(3^3))^7 (iii) (11^(1/2))/(11^(1/4)) (iv) 7^(1/2). 8^(1/2)

Prove that (3+i)/(1+2i)+(3-i)/(1-2i) is a real number.

Simplify the following: (5i)(-(3)/(5)i)

Simplify the following: (2i)^(3)