Step 1a

Write down the expression:
\$(a + bi) \times (c - di)\$

Distribute each term in the first complex number across each term in the second complex number:
\$a \times c + a \times (−di) + bi \times c + bi \times (−di)\$

Perform each multiplication:
Multiply the real parts:
\$a \times c = ac\$

Multiply the real part of the first number by the imaginary part of the second number:
\$a \times (-di) = -adi\$

Multiply the imaginary part of the first number by the real part of the second number:
\$bi \times c = bci\$

Multiply the imaginary parts:
\$bi \times (-di) =-bdi^2\$
Recall that i^2 = -1, so: \$-bdi^2 = -bd(-1) = bd\$

Combine all the results:
ac - adi + bci + bd

Combine the real and imaginary parts:
=(ac + bd) + (bc − ad)i

Explanation: To multiply the complex numbers (a + bi) and (c − di), distribute each term and combine like terms, simplifying using \$i^2 =−1\$, resulting in (ac + bd) + (bc − ad)i.