MATH SOLVE

3 months ago

Q:
# What is the value of the product 3-2i3+2i ？ 5 9+4i 9-4i 13

Accepted Solution

A:

(A)Expand the expression using (a-b)(a+b)=a^2-b^2: 3^{2} - (2 i)^{2}Simplify using exponent rule with same exponent (ab)^{n}=a^{n}\cdot b^{n}: 3^{2} - 2^{2} \times i^{2}Calculate the power: 9 - 4 \times i^{2}Rewrite by definition i^2=-1: 9 - 4 \times (-1)Calculate the product or quotient: 9 + 4Calculate the sum or difference: 13Match the option between 13 and 5:: False(B)Expand the expression using (a-b)(a+b)=a^2-b^2: 3^{2} - (2 i)^{2}Simplify using exponent rule with same exponent (ab)^{n}=a^{n}\cdot b^{n}: 3^{2} - 2^{2} \times i^{2}Calculate the power: 9 - 4 \times i^{2}Rewrite by definition i^2=-1: 9 - 4 \times (-1)Calculate the product or quotient: 9 + 4Calculate the sum or difference: 13Match the option between 13 and 9+4i:: False(C)Expand the expression using (a-b)(a+b)=a^2-b^2: 3^{2} - (2 i)^{2}Simplify using exponent rule with same exponent (ab)^{n}=a^{n}\cdot b^{n}: 3^{2} - 2^{2} \times i^{2}Calculate the power: 9 - 4 \times i^{2}Rewrite by definition i^2=-1: 9 - 4 \times (-1)Calculate the product or quotient: 9 + 4Calculate the sum or difference: 13Match the option between 13 and 9-4i:: False(D)Expand the expression using (a-b)(a+b)=a^2-b^2: 3^{2} - (2 i)^{2}Simplify using exponent rule with same exponent (ab)^{n}=a^{n}\cdot b^{n}: 3^{2} - 2^{2} \times i^{2}Calculate the power: 9 - 4 \times i^{2}Rewrite by definition i^2=-1: 9 - 4 \times (-1)Calculate the product or quotient: 9 + 4Calculate the sum or difference: 13Match the option between 13 and 13:: True