What is (3i-2j+k)2(-5i-j+7k) ?

The solution to (3i-2j+k)2(-5i-j+7k) is (4j^2-30jk+14k^2+30)+(14j+32k)i

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simplify (3i-2j+k)2(-5i-j+7k)

simplify

(3 i - 2 j + k) 2 (- 5 i - j + 7 k)

(4 j^{2} - 30 jk + 14 k^{2} + 30) + (14 j + 32 k) i

Solution steps

(3 i - 2 j + k) \cdot 2 (- 5 i - j + 7 k)

Rewrite

3 i - 2 j + k

in standard complex form:

(- 2 j + k) + 3 i

Rewrite

- 5 i - j + 7 k

in standard complex form:

(- j + 7 k) - 5 i

= ((- 2 j + k) + 3 i) \cdot 2 ((- j + 7 k) - 5 i)

Apply complex arithmetic rule:

(a + bi) (c + d i) = (a c - b d) + (a d + b c) i

= (((- 2 j + k) (- j + 7 k) - 3 (- 5)) + ((- 2 j + k) (- 5) + 3 (- j + 7 k)) i) \cdot 2

Simplify

((- 2 j + k) (- j + 7 k) - 3 (- 5)) + ((- 2 j + k) (- 5) + 3 (- j + 7 k)) i : (2 j^{2} - 15 jk + 7 k^{2} + 15) + (7 j + 16 k) i

= ((2 j^{2} - 15 jk + 7 k^{2} + 15) + (7 j + 16 k) i) \cdot 2

Expand

((2 j^{2} - 15 jk + 7 k^{2} + 15) + (7 j + 16 k) i) \cdot 2 : 4 j^{2} - 30 jk + 14 k^{2} + 30 + 14 ji + 32 ki

= 4 j^{2} - 30 jk + 14 k^{2} + 30 + 14 ji + 32 ki

Rewrite in standard complex form:

(4 j^{2} - 30 jk + 14 k^{2} + 30) + (14 j + 32 k) i

= (4 j^{2} - 30 jk + 14 k^{2} + 30) + (14 j + 32 k) i

\frac{( e + 1 ) ( e - 1 )}{1 + e ^{2}}

(x^{\frac{5}{2}} - y^{\frac{1}{4}}) (x^{\frac{5}{2}} + y^{\frac{1}{4}})

(2 x + y) d x

(2 x + y) d y

e^{(2 + 3 i) t}

What is (3i-2j+k)2(-5i-j+7k) ?
The solution to (3i-2j+k)2(-5i-j+7k) is (4j^2-30jk+14k^2+30)+(14j+32k)i