# Complex Number Kookiness 4

## Examples:

(7 + 8i)(8 + 7i) = 113i

(√(113) = the absolute value of both of these complex numbers!)

(3 - 2i)(-2 + 3i) = 13i

(√(13) = the absolute value of both of these complex numbers!)

(-3 - 2i)(-2 - 3i) = 13i

(√(13) = the absolute value of both of these complex numbers!)

(3 + 4i)(4 + 3i) = 25i

(5 = the absolute value of both of these complex numbers!)

(1 + i)(1 + i) = (1 + i)2= 2i

(√(2) = the absolute value of both of these complex numbers! Wait a minute, they're the exact same complex number!)

Whenever you multiply 2 complex numbers with the real & imaginary values swapped, their product will always be equal to the square of their shared absolute value multiplied by the imaginary unit i, even if either the value of a or b is negative! If a = b, then the absolute value of a complex number will be equal to a multiple of the square root of 2.

(5 + 5i)(5 + 5i) = (5 + 5i)2= 50i

(5√(2) = the absolute value of both of these complex numbers! Wait a minute, they're the exact same complex number!)

(5 - 5i)(-5 + 5i) = 50i

(5√(2) = the absolute value of both of these complex numbers!)

(-5 - 5i)(-5 - 5i) = (-5 - 5i)2= 50i

(5√(2) = the absolute value of both of these complex numbers! Wait a minute, they're the exact same complex number!)