Step 1a

Identify the complex conjugate of the denominator:
The complex conjugate of (1 - i) is (1 + i)

Multiply both the numerator and denominator by the complex conjugate:
3 + 2i)(1 + i/1 - i)(1 + i

Expand the numerator:
\$(3 \times 1) + (3 \times i) + (2i \times 1) + (2i \times i)\$
\$3 + 3i + 2i + 2i^2\$
3 + 5i - 2 (since \$i^2 = -1\$)
= 1 + 5i

Expand the denominator:
(1 \times 1) + (1 \times i) + (-i \times 1) + (-i \times i)
\$1 + i - i - i^2\$
1 + 1 (since \$i^2 = -1\$)
= 2

Simplify the fraction:
\$(1 + 5i)/2\$

Separate into real and imaginary parts:
\$1/2 + (5/2)i\$

Explanation: To divide \$(3 + 2i)/(1 - i)\$, multiply the numerator and denominator by the conjugate of the denominator, simplify, and combine terms to obtain \$1/2 + (5/2)i\$.