IMAGINARY AND COMPLEX NUMBERS Higher Concepts of Mathematics Imaginary numbers are added or subtracted by writing them using the imaginary unit i and then adding  or  subtracting  the  real  number  coefficients  of  i.    They  are  added  or  subtracted  like algebraic terms in which the imaginary unit i is treated like a literal number.  Thus, and 25 9 are added by writing them as 5i and 3i and adding them like algebraic terms.   The result is 8i which  equals or .   Similarly, subtracted  from equals  3i  subtracted 8 1 64 9 25 from 5i which equals 2i or or . 2 1 4 Example: Combine the following imaginary numbers: Solution: 16   36   49   1 16   36   49   1 4i      6i      7i      i 10i      8i 2i Thus, the result is  2i      2 1     4 Imaginary numbers are multiplied or divided by writing them using the imaginary unit i, and then multiplying or dividing them like algebraic terms.  However, there are several basic relationships which must also be used to multiply or divide imaginary numbers. i² = (i)(i) = = -1 ( 1  ) ( 1  ) i³ = (i²)(i) = (-1)(i) = -i i⁴ = (i²)(i²) = (-1)(-1) = +1 Using  these  basic  relationships,  for  example, equals  (5i)(2i)  which  equals  10i². ( 25) ( 4  ) But, i² equals -1.   Thus, 10i² equals (10)(-1) which equals -10. Any square root has two roots, i.e., a statement x² = 25 is a quadratic and has roots x = ±5 since +5² = 25 and (-5) x (-5) = 25. MA-05 Page 12 Rev. 0