Simplify the expression to a + bi form: (1+i)(9+8i) Answer:

Apply Distributive Property: Apply the distributive property (also known as the FOIL method for binomials) to multiply the two complex numbers. (1+i)(9+8i) = 1*(9+8i) + i*(9+8i)Multiply Real and Imaginary Parts: Multiply the real part of the first complex number by both the real and imaginary parts of the second complex number. 1*(9+8i) = 9 + 8iReplace i^2 with -1: Multiply the imaginary part of the first complex number by both the real and imaginary parts of the second complex number. i*(9+8i) = 9i + 8i^2Simplify Expression: Remember that i^2 = -1. Replace i^2 with -1 in the expression. 9i + 8i^2 = 9i + 8(-1)Combine Real and Imaginary Parts: Simplify the expression by combining like terms and performing the multiplication. 9i + 8(-1) = 9i - 8Final Expression in a + bi Form: Combine the results from Step 2 and Step 5 to get the final expression in a + bi form. (9 + 8i) + (9i - 8) = 9 - 8 + 8i + 9iCombine Parts: Combine the real parts and the imaginary parts. 9 - 8 + 8i + 9i = 1 + 17i

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Simplify the expression to a + bi form:

(1+i)(9+8i)
Answer:

Simplify the expression to a + bi form: $\newline$ $(1+i)(9+8 i)$ $\newline$ Answer:

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Q. Simplify the expression to a + bi form:

\newline

(1+i)(9+8 i)

\newline

Answer:

Apply Distributive Property: Apply the distributive property (also known as the FOIL method for binomials) to multiply the two complex numbers. $\newline$ $(1+i)(9+8i) = 1\times(9+8i) + i\times(9+8i)$
Multiply Real and Imaginary Parts: Multiply the real part of the first complex number by both the real and imaginary parts of the second complex number. $\newline$ $1\times(9+8i) = 9 + 8i$
Replace $i^2$ with $-1$ : Multiply the imaginary part of the first complex number by both the real and imaginary parts of the second complex number. $\newline$ $i*(9+8i) = 9i + 8i^2$
Simplify Expression: Remember that $i^2 = -1$ . Replace $i^2$ with $-1$ in the expression. $\newline$ $9i + 8i^2 = 9i + 8(-1)$
Combine Real and Imaginary Parts: Simplify the expression by combining like terms and performing the multiplication. $\newline$ $9i + 8(-1) = 9i - 8$
Final Expression in $a + bi$ Form: Combine the results from Step $2$ and Step $5$ to get the final expression in $a + bi$ form. $\newline$ $(9 + 8i) + (9i - 8) = 9 - 8 + 8i + 9i$
Combine Parts: Combine the real parts and the imaginary parts. $9 - 8 + 8i + 9i = 1 + 17i$