Simplify the expression to a + bi form: (-9-7i)(3+6i) 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. (-9-7i)(3+6i) = (-9 * 3) + (-9 * 6i) + (-7i * 3) + (-7i * 6i)Calculate Each Part: Now, we calculate each part of the expression separately. (-9 * 3) = -27 (-9 * 6i) = -54i (-7i * 3) = -21i (-7i * 6i) = -42i^2 (Remember that i^2 = -1)Combine Real and Imaginary Parts: Next, we combine the real parts and the imaginary parts and simplify using i^2 = -1. Real part: -27 Imaginary part: -54i - 21i = -75i And for the term with i^2: -42i^2 = -42(-1) = 42Add Real and Imaginary Parts: Now, we add the real part and the simplified term with i^2 together, and then combine it with the imaginary part. Real part: -27 + 42 = 15 Imaginary part: -75i So, the expression in a + bi form is 15 - 75i.

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Q. Simplify the expression to a + bi form:

\newline

(-9-7 i)(3+6 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. $\newline$ $(-9-7i)(3+6i) = (-9 \times 3) + (-9 \times 6i) + (-7i \times 3) + (-7i \times 6i)$
Calculate Each Part: Now, we calculate each part of the expression separately. $\newline$ $(-9 \times 3) = -27$ $\newline$ $(-9 \times 6i) = -54i$ $\newline$ $(-7i \times 3) = -21i$ $\newline$ $(-7i \times 6i) = -42i^2$ (Remember that $i^2 = -1$ )
Combine Real and Imaginary Parts: Next, we combine the real parts and the imaginary parts and simplify using $i^2 = -1$ .
Real part: $-27$
Imaginary part: $-54i - 21i = -75i$
And for the term with $i^2$ : $-42i^2 = -42(-1) = 42$
Add Real and Imaginary Parts: Now, we add the real part and the simplified term with $i^2$ together, and then combine it with the imaginary part. $\newline$ Real part: $-27 + 42 = 15$ $\newline$ Imaginary part: $-75i$ $\newline$ So, the expression in $a + bi$ form is $15 - 75i$ .