Question

c. state the domain and range of the inverse function.\
8 - 69.\
multiply and simplify each expression. homework help\
\xa0\xa0\xa0\xa0a. $(3 + 2i)(4 + i)$\
\xa0\xa0\xa0\xa0b. $(2 + 3i)(2 - 3i)$\
\xa0\xa0\xa0\xc. $(5 - 2i)(5 + 2i)$\
\xa0\xa0\xa0\xd. $(a + bi)(a - bi)$

Explanation:

Step1: Multiply using distributive property

$(3+2i)(4+i)=3*4 + 3*i + 2i*4 + 2i*i$

Step2: Simplify terms with $i^2=-1$

$=12 + 3i + 8i + 2(-1)$

Step3: Combine like terms

$=12-2 + (3i+8i)=10 + 11i$

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Step1: Multiply using distributive property

$(2+3i)(2-3i)=2*2 - 2*3i + 3i*2 - 3i*3i$

Step2: Simplify terms with $i^2=-1$

$=4 - 6i + 6i - 9(-1)$

Step3: Combine like terms

$=4+9 + (-6i+6i)=13$

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Step1: Multiply using distributive property

$(5-2i)(5+2i)=5*5 + 5*2i - 2i*5 - 2i*2i$

Step2: Simplify terms with $i^2=-1$

$=25 + 10i - 10i - 4(-1)$

Step3: Combine like terms

$=25+4 + (10i-10i)=29$

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Step1: Multiply using distributive property

$(a+bi)(a-bi)=a*a - a*bi + bi*a - bi*bi$

Step2: Simplify terms with $i^2=-1$

$=a^2 - abi + abi - b^2(-1)$

Step3: Combine like terms

$=a^2 + b^2 + (-abi+abi)=a^2 + b^2$

Answer:

a. $10 + 11i$
b. $13$
c. $29$
d. $a^2 + b^2$