Question

(-5+ i)(12- i)(-3).

Answer 1

177 - 51i

Explanation:

`(-5+ i)(12- i)(-3).`

`(-5+ i)(12- i)`

Apply the distributive property

`-5X12-5(-i)`+
`(-i)X12+(i)`
`(-i)`

Simplify

`-60+5i+12i-1i^(2)`

Reduce the imaginary units using the property
`i^(2) =-1`

`-60+5i+12i-1(-1)`

Simplify and write in the standard form of
`a+bi`

`-59+17i\\(-59+17i)(-3)\\177-51i`

Hope it helps u:)

Answer 2

`177 - 51i`

Explanation:

Given expression:

`(-5+i)(12-i)(-3)`

Use the FOIL method to multiply the first two parentheses:

`\implies \left(-5 \cdot 12 -5 \cdot -i +i \cdot 12 + i \cdot -i\right)(-3)`

`\implies \left(-60 +5i +12i -i^2\right)(-3)`

`\implies \left(-60 +17i -i^2\right)(-3)`

Multiply:

`\implies -60 \cdot -3 +17i \cdot -3 -i^2 \cdot -3`

`\implies 180-51i+3i^2`

Apply the imaginary number rule: i² = -1

`\implies 180-51i+3(-1)`

Simplify:

`\implies 180-51i-3`

`\implies 177-51i`