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Multiply and simplify the following complex numbers: $(3-4i) \times (-3 + 2i)$

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Evaluate integers raised to rational exponents

Full solution

Q. Multiply and simplify the following complex numbers:

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

Apply Distributive Property: Step $1$ : Apply the distributive property to multiply the complex numbers. $\newline$ $(3-4i) \times (-3+2i) = 3\times(-3) + 3\times(2i) - 4i\times(-3) - 4i\times(2i)$
Perform Multiplication: Step $2$ : Perform the multiplication for each term. $\newline$ = $-9 + 6i + 12i - 8i^2$
Combine Like Terms: Step $3$ : Combine like terms and remember that $i^2 = -1$ .
= $-9 + 18i - 8(-1)$
Simplify Expression: Step $4$ : Simplify the expression by substituting $i^2$ with $-1$ . $\newline$ $= -9 + 18i + 8$
Add Real and Imaginary Parts: Step $5$ : Add the real parts and combine the imaginary parts. $\newline$ $= -1 + 18i$

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