Question

multiply complex numbers as you would multiply polynomials. remember $i^2 = -1$.

1. $-4i(3-2i)$
2. $(4-5i)(3+2i)$

Explanation:

Step1: Distribute $-4i$ to terms

$-4i \times 3 + (-4i) \times (-2i)$

Step2: Calculate each product

$-12i + 8i^2$

Step3: Substitute $i^2=-1$

$-12i + 8(-1)$

Step4: Simplify the expression

$-8 - 12i$

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Step1: Expand using FOIL method

$4\times3 + 4\times2i -5i\times3 -5i\times2i$

Step2: Calculate each product

$12 + 8i -15i -10i^2$

Step3: Combine like terms

$12 -7i -10i^2$

Step4: Substitute $i^2=-1$

$12 -7i -10(-1)$

Step5: Simplify the expression

$12 -7i +10 = 22 -7i$

Answer:

1. $\boldsymbol{-8 - 12i}$
2. $\boldsymbol{22 - 7i}$