Simplify the expression to a + bi form: (-11+4i)(10+7i) Answer:

Multiply Real Parts: We need to multiply two complex numbers (-11+4i) and (10+7i) using the distributive property (also known as the FOIL method for binomials).Multiply Real and Imaginary: First, we multiply the real parts: (-11) * (10) = -110.Combine Real and Imaginary: Next, we multiply the real part of the first complex number by the imaginary part of the second: (-11) * (7i) = -77i.Final Expression: Then, we multiply the imaginary part of the first complex number by the real part of the second: (4i) * (10) = 40i.Finally, we multiply the imaginary parts: (4i) * (7i) = 28i^2. Since i^2 = -1, this becomes 28 * (-1) = -28.Now, we combine all the parts: real with real and imaginary with imaginary. Real: -110 + (-28) = -138. Imaginary: -77i + 40i = -37i.The expression in a + bi form is: -138 - 37i.

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Simplify the expression to a + bi form:

(-11+4i)(10+7i)
Answer:

Simplify the expression to a + bi form: $\newline$ $(-11+4 i)(10+7 i)$ $\newline$ Answer:

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Algebra 2

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Q. Simplify the expression to a + bi form:

\newline

(-11+4 i)(10+7 i)

\newline

Answer:

Multiply Real Parts: We need to multiply two complex numbers $(-11+4i)$ and $(10+7i)$ using the distributive property (also known as the FOIL method for binomials).
Multiply Real and Imaginary: First, we multiply the real parts: $(-11) \times (10) = -110$ .
Combine Real and Imaginary: Next, we multiply the real part of the first complex number by the imaginary part of the second: $(-11) \times (7i) = -77i$ .
Final Expression: Then, we multiply the imaginary part of the first complex number by the real part of the second: $(4i) \times (10) = 40i$ .
Final Expression: Then, we multiply the imaginary part of the first complex number by the real part of the second: $(4i) \times (10) = 40i$ .Finally, we multiply the imaginary parts: $(4i) \times (7i) = 28i^2$ . Since $i^2 = -1$ , this becomes $28 \times (-1) = -28$ .
Final Expression: Then, we multiply the imaginary part of the first complex number by the real part of the second: $(4i) \times (10) = 40i$ .Finally, we multiply the imaginary parts: $(4i) \times (7i) = 28i^2$ . Since $i^2 = -1$ , this becomes $28 \times (-1) = -28$ .Now, we combine all the parts: real with real and imaginary with imaginary. $\newline$ Real: $-110 + (-28) = -138$ . $\newline$ Imaginary: $-77i + 40i = -37i$ .
Final Expression: Then, we multiply the imaginary part of the first complex number by the real part of the second: $(4i) \times (10) = 40i$ .Finally, we multiply the imaginary parts: $(4i) \times (7i) = 28i^2$ . Since $i^2 = -1$ , this becomes $28 \times (-1) = -28$ .Now, we combine all the parts: real with real and imaginary with imaginary. $\newline$ Real: $-110 + (-28) = -138$ . $\newline$ Imaginary: $-77i + 40i = -37i$ .The expression in $a + bi$ form is: $-138 - 37i$ .