Simplify (12 – 6i) – (-3 – 8i)?

3 Answers

• First question:

  We change the sign of the second parenthesis so that the minus changes into plus

  ( 12 – 6i ) + ( 3 + 8i )

  Now we remove the parenthesis as they are useless now

  12 – 6i + 3 + 8i = 2i + 15

  Second question:

  we multiply each item in the first parenthesis with two items of the second parenthesis

  ( 6*8 ) + ( -18i ) + ( 8i ) + ( -3i^2 )

  Now we remove parenthesis and do operations

  -3i – 10i + 48

  Third question:

  we divide both by 2

  SQRT(x-8) = 3

  We raise both sides to the power of 2

  x-8 = 9

  we add 8 to both sides

  x = 17

  The last one:

  We raise both sides to the power of 2

  X + 14 + 2 = X^2

  we subtract (X + 14 + 2) from both sides

  X^2 – X – 16 = 0

  I can’t find any simpler forms.

• 1. Treat as vector addition (12, -6i) + (3, 8i) = (15, -2i) = 15 – 2i

  2. (6+i) * (8-3i) = 48 + 8i – 18i – 3i² = 48 + 8i – 18i + 3 = 51 – 10i

  3. 2 * SQRT[ x – 8 ] = 6, SQRT[ x – 8 ] = 3, x – 8 = 9, x = 17

  4 SQRT[ x + 14 + 2 ] = SQRT[ x + 16 ] = x, x² – x – 16 = 0

  By the quadratic formula, x = 1/2 ± 1/2 * SQRT[ 1 + 64 ] = 1/2 ± 1/2 * SQRT[ 65 ]

• well the first is

  (12-8i)-(-3-8i)=

  12+3-8i+8i=15

  2nd is (6+i)(8-3i)=

  6(8-3i)i(8-3i)=

  48-18i+8i-3isquared=

  48+3-18i+8i=

  51-10i hope that helps!

  Don’t know bout the others!