How do you simplify (7i)-(2i)-(8-7i)? (3i)(6i)(-8+4i)? 4i/8-3i? 2-7i/-5-7i?

Question

 Simplify help

Answer 1

1.   (7i)-(2i)-(8-7i)

     = 7i - 2i - 8 + 7i

     = 12i -8

 

2.   (3i)(6i)(-8+4i)

     = [3(6)(i²)](-8 + 4i)

     = [18(-1)](-8 + 4i)

     = -18(-8 + 4i)

     = 144 - 72i

 

3.   4i/8-3i

     = 4i(8+3i)/[(8-3i)(8+3i)]

     = (32i +12i²)/(64 -9i²)

     = (32i-12)/(64+9)

     = (-12 + 32i)/73

 

4.    2-7i/-5-7i

      = [(2-7i)(-5+7i)]/[(-5-7i)(-5+7i)]

      = [2(-5)+2(7i)-(7i)(-5)-49i²]/[(-5)(-5)-35i+35i-49i²]

      = (-10 + 14i + 35i + 49)/(25+49)

      = (39 + 49i)/74

Answer 2

First problem

 

7i - 2i -8 + 7i

 

= 12i - 8

 

2) 4i / ( 8. - 3i )

 

4i ( 8 + 3i) / (8-3i)(8+3i)

 

= ( 64 - 9(-1)) / ( 64 - 9(-1))

 

= 73 / 73

 

= 1

 

3) (2 - 7i ) / ( - 5 - 7i)

 

= (2-7i)(2+7i)  / ( -5-7i)(-5+7i)

 

= ( 4 - 49(-1)) / (25 - 49(-1))

 

= 53 / 74

 

the last two problems used the conjugate for, where we had to multiply top and bottom by the conjugate in order to convert the equation to standard form and the very first problem just used combining like terms and the distributive property. Hope it helped good luck