Multiply the following complex numbers ( -16 + 2i) and ( 8 - 8i).

The given expression

( -16 + 2i) and ( 8 - 8i)

Apply the distributive property (FOIL method):

\$- 16 times 8 - 16 times ( - 8i) + 2i times 8 + 2i times (-8i)\$

Calculate each term:

\$- 128 + 128i + 16i - 16i^2\$

Since \$i^2 = - 1\$.

Plug the \$i^2 = - 1\$ in the above expression and then simplify it:

\$ - 128 + 144i - 16 times (-1)\$

⇒ - 128 + 144i + 16

⇒ - 112 + 144i

Therefore the multiply of complex numbers is - 112 + 144i.

This result does not match our calculation because the signs of the real parts are incorrect. In the correct solution, the real part is −112, not 112

112 + 144i

Wrong: Because the real part of the product is - 112 (not 121), and the imaginary part is 144i (not - 144i)

121 - 144i

The calculation of complex numbers confirms the accuracy of this option, making it the correct choice

-112 + 144i i

The real part should be −112, not −121. So, this is option is wrong

-121 + 144i

Option

C

Can you summarize what you’ve understood in the above steps?