Multiply 2 + 3i and 9 + -8i

a = bi = <-- Enter a and bi piece
c = di = <-- Enter c and di piece (not needed for square root or absolute value or conjugate)

Perform the complex number multiplication: (2 + 3i)(9 - 8i)

The formula for this using the FOIL method is: (a * c) + (b * c) + (a * d) + (b * d) where:
a = 2, b = 3, c = 9, and d = -8

Now plug these values into our formula and evaluate:
(2 + 3i)(9 - 8i) = (2 * 9) + (3i * 9) + (2 * -8i) + (3i * -8i)
(2 + 3i)(9 - 8i) = 18 + 27i - 16i - 24i2

Group the like terms that contain i:
(2 + 3i)(9 - 8i) = 18 + (27 - 16)i - 24i2
(2 + 3i)(9 - 8i) = 18 + 11i - 24i2

Simplify our last term:
i2 = √-1 * √-1 = -1, so our last term becomes:
(2 + 3i)(9 - 8i) = 18 + 11i - 24* (-1)
(2 + 3i)(9 - 8i) = 18 + 11i + 24

Now group the 2 constants and finalize our answer
(2 + 3i)(9 - 8i) = (18 + 24) + 11i
(2 + 3i)(9 - 8i) = 42 + 11i