Simplify the expression to a + bi form: (-1+9i)(11-7i) Answer:

Apply Distributive Property: First, we need to apply the distributive property (also known as the FOIL method for binomials) to multiply the two complex numbers. This involves multiplying each term in the first complex number by each term in the second complex number.Multiply Real Parts: Multiply the real parts: (-1) * (11) = -11.Multiply Outer Terms: Multiply the outer terms: (-1) * (-7i) = 7i.Multiply Inner Terms: Multiply the inner terms: (9i) * (11) = 99i.Multiply Imaginary Parts: Multiply the imaginary parts: (9i) * (-7i) = -63i^2. Since i^2 = -1, this becomes -63 * (-1) = 63.Combine Like Terms: Now, combine the like terms: the real parts (-11 and 63) and the imaginary parts (7i and 99i).Combine Real Parts: Combine the real parts: -11 + 63 = 52.Combine Imaginary Parts: Combine the imaginary parts: 7i + 99i = 106i.Write Final Answer: Write the final answer in a + bi form: 52 + 106i.

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Q. Simplify the expression to a + bi form:

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(-1+9 i)(11-7 i)

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Answer:

Apply Distributive Property: First, we need to apply the distributive property (also known as the FOIL method for binomials) to multiply the two complex numbers. This involves multiplying each term in the first complex number by each term in the second complex number.
Multiply Real Parts: Multiply the real parts: $(-1) \times (11) = -11$ .
Multiply Outer Terms: Multiply the outer terms: $(-1) \times (-7i) = 7i$ .
Multiply Inner Terms: Multiply the inner terms: $(9i) \times (11) = 99i$ .
Multiply Imaginary Parts: Multiply the imaginary parts: $9i$ * $-7i$ = (-63\)i^ $2$ . Since $i^2 = -1$ , this becomes (-63\) * $-1$ = ${63}$ .
Combine Like Terms: Now, combine the like terms: the real parts ( $-11$ and $63$ ) and the imaginary parts ( $7i$ and $99i$ ).
Combine Real Parts: Combine the real parts: $-11 + 63 = 52$ .
Combine Imaginary Parts: Combine the imaginary parts: $7i + 99i = 106i$ .
Write Final Answer: Write the final answer in $a + bi$ form: $52 + 106i$ .