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Mamont248 [21]
3 years ago
11

Simplify the expression. -5+i/2i

Mathematics
1 answer:
Lostsunrise [7]3 years ago
7 0

Answer:

\rm - \dfrac{11}{2}

Step-by-step explanation:

\rm Simplify \:  the  \: following: \\   \rm \longrightarrow - 5 +  \dfrac{i}{2} i \\  \\  \rm Combine \:  powers. \\  \rm  \dfrac{i \times i}{2}  =  \dfrac{i^{1 + 1}}{2}: \\  \rm \longrightarrow  - 5 +  \dfrac{i^{1 + 1}}{2}  \\  \\  \rm 1 + 1 = 2: \\ \rm \longrightarrow  - 5 +  \dfrac{i^2}{2}  \\  \\  \rm i^2 = -1: \\ \rm \longrightarrow  - 5 +   \dfrac{( - 1)}{2}   \\  \\  \rm \longrightarrow  - 5 -  \dfrac{1}{2}   \\  \\  \rm Put   \:   - 5 -  \dfrac{1}{2}   \: over  \: the  \: common \:  denominator  \: 2.  \\  \rm   - 5 -  \dfrac{1}{2}   =  \dfrac{2( -  5)}{2} -  \dfrac{1}{2}  : \\   \rm \longrightarrow  \dfrac{ - 5 \times 2}{2}  -  \dfrac{1}{2}  \\  \\  \rm 2 (-5) = -10: \\    \rm \longrightarrow    \dfrac{ - 10}{2}  -  \dfrac{1}{2}  \\  \\  \rm \dfrac{ - 10}{2}  -  \dfrac{1}{2}  =  \dfrac{ - 10 - 1}{2} : \\   \rm \longrightarrow \dfrac{ - 10 - 1}{2}  \\  \\  \rm -10 - 1 = -11: \\    \rm \longrightarrow  -  \dfrac{11}{2}

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