(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!)
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© Derek Cumberbatch