Complex Numbers!?

Question

I need help with these problems! 
[7+9i] + [-5i]= 
[12 +5i] - [ 2 - i ]= 
[8 + i][ 2 + 7i ]= 
[-6i]^2 
[9 + 4i]^2 
[2 + i][4 - 5i ] 
Complex factors of x^2 + 16 

Answer 1

(1)

(7+9i)+(-5i)

= 7+9i-5i

= 7+i(9-5)

=7+4i

 

(2)

[12 +5i] - [ 2 - i ]

=12+5i-2+i

=10+i(5+1)

=10+6i

 

(3)

[8 + i][ 2 + 7i ]

(a+b)(c+d) = ac+ad+bc+bd

[8 + i][ 2 + 7i ] = 16 + 56i + 2i + i×7i

                      =16 +58i +7i²

                      =16+58i +7(-1)             ( since i² =-1)

                      =16+58i-7

                      = 9+58i

Answer 2

(4)

[-6i]² = 36i²

        =36×(-1)

       = -36

 

(5)

[9 + 4i]²

= 9² + (4i)² + 2×9×4i           { (a+b)² =a²+b²+2ab }

=81 +16i² +72i

=81 +16(-1) +72i

=81 -16+72i

=65 +72i

 

(6)

[2 + i][4 - 5i ]

= 8-10i+4i-5i²

=8-6i-5(-1)

=8-6i+5

=13-6i

 

(7)

x² +16 =0

x² = -16

x = √(-16)

x = √(16i²)

x = ± 4i

factors are ± 4i

Factor form (x+4i)(x-4i)