Simplify the expression to a + bi form: (7+2i)(-8-3i) Answer:

Apply Distributive Property: To multiply two complex numbers, we use the distributive property (also known as the FOIL method for binomials), which states that for any complex numbers (a + bi) and (c + di), the product is (ac - bd) + (ad + bc)i. Let's apply this to (7 + 2i)(-8 - 3i). First, we multiply the real parts: 7 * (-8) = -56.Multiply Real Parts: Next, we multiply the imaginary parts: 2i * (-3i) = -6i^2. Since i^2 = -1, this simplifies to -6 * (-1) = 6.Multiply Imaginary Parts: Now, we multiply the outer terms: 7 * (-3i) = -21i.Multiply Outer Terms: Finally, we multiply the inner terms: 2i * (-8) = -16i.Multiply Inner Terms: We combine all these results: (-56 + 6) + (-21i - 16i).Combine Results: Simplify the real parts and the imaginary parts separately: (-56 + 6) = -50 and (-21i - 16i) = -37i.Simplify Real and Imaginary Parts: Combine the simplified real and imaginary parts to get the expression in a + bi form: -50 - 37i.

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Q. Simplify the expression to a + bi form:

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(7+2 i)(-8-3 i)

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Answer:

Apply Distributive Property: To multiply two complex numbers, we use the distributive property (also known as the FOIL method for binomials), which states that for any complex numbers $(a + bi)$ and $(c + di)$ , the product is $(ac - bd) + (ad + bc)i$ . Let's apply this to $(7 + 2i)(-8 - 3i)$ . First, we multiply the real parts: $7 \times (-8) = -56$ .
Multiply Real Parts: Next, we multiply the imaginary parts: $2i \times (-3i) = -6i^2$ . Since $i^2 = -1$ , this simplifies to $-6 \times (-1) = 6$ .
Multiply Imaginary Parts: Now, we multiply the outer terms: $7 \times (-3i) = -21i$ .
Multiply Outer Terms: Finally, we multiply the inner terms: $2i \times (-8) = -16i$ .
Multiply Inner Terms: We combine all these results: $(-56 + 6) + (-21i - 16i)$ .
Combine Results: Simplify the real parts and the imaginary parts separately: $(-56 + 6) = -50$ and $(-21i - 16i) = -37i$ .
Simplify Real and Imaginary Parts: Combine the simplified real and imaginary parts to get the expression in $a + bi$ form: $-50 - 37i$ .