Solve ( - 5j^49j^32j-3) ( - 3j^4-8j^29j 8) - ScanMath

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Type your math problem... ( - 5j^49j^32j-3) ( - 3j^4-8j^29j 8)

Question

Simplify the expression

270 j^{12} + 51840 j^{11} + 9 j^{4} + 1728 j^{3}

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Factor the expression

9 j^{3} (30 j^{8} + 1) (j + 192)

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Find the roots

j_{1} = - 192, j_{2} = 0, j_{3} = - \frac{8 2040 \times 2700 0 ^{2} + 1440 \times 2700 0 ^{2} 2}{60} + \frac{8 2040 \times 2700 0 ^{2} - 1440 \times 2700 0 ^{2} 2}{60} i, j_{4} = \frac{8 2040 \times 2700 0 ^{2} + 1440 \times 2700 0 ^{2} 2}{60} - \frac{8 2040 \times 2700 0 ^{2} - 1440 \times 2700 0 ^{2} 2}{60} i

Alternative Form

j_{1} = - 192, j_{2} = 0, j_{3} \approx - 0.603914 + 0.250149 i, j_{4} \approx 0.603914 - 0.250149 i

Evaluate

(- 5 j^{4} \times 9 j^{3} \times 2 j - 3) (- 3 j^{4} - 8 j^{2} \times 9 j \times 8)

To find the roots of the expression,set the expression equal to 0

(- 5 j^{4} \times 9 j^{3} \times 2 j - 3) (- 3 j^{4} - 8 j^{2} \times 9 j \times 8) = 0

Multiply

More Steps

(- 90 j^{8} - 3) (- 3 j^{4} - 8 j^{2} \times 9 j \times 8) = 0

Multiply

More Steps

(- 90 j^{8} - 3) (- 3 j^{4} - 576 j^{3}) = 0

Change the sign

(90 j^{8} + 3) (- 3 j^{4} - 576 j^{3}) = 0

Separate the equation into 2 possible cases

90 j^{8} + 3 = 0 - 3 j^{4} - 576 j^{3} = 0

Solve the equation

More Steps

j = \frac{8 2040 \times 2700 0 ^{2} + 1440 \times 2700 0 ^{2} 2}{60} - \frac{8 2040 \times 2700 0 ^{2} - 1440 \times 2700 0 ^{2} 2}{60} i j = - \frac{8 2040 \times 2700 0 ^{2} + 1440 \times 2700 0 ^{2} 2}{60} + \frac{8 2040 \times 2700 0 ^{2} - 1440 \times 2700 0 ^{2} 2}{60} i - 3 j^{4} - 576 j^{3} = 0

Solve the equation

More Steps

j = \frac{8 2040 \times 2700 0 ^{2} + 1440 \times 2700 0 ^{2} 2}{60} - \frac{8 2040 \times 2700 0 ^{2} - 1440 \times 2700 0 ^{2} 2}{60} i j = - \frac{8 2040 \times 2700 0 ^{2} + 1440 \times 2700 0 ^{2} 2}{60} + \frac{8 2040 \times 2700 0 ^{2} - 1440 \times 2700 0 ^{2} 2}{60} i j = 0 j = - 192

Solution

j_{1} = - 192, j_{2} = 0, j_{3} = - \frac{8 2040 \times 2700 0 ^{2} + 1440 \times 2700 0 ^{2} 2}{60} + \frac{8 2040 \times 2700 0 ^{2} - 1440 \times 2700 0 ^{2} 2}{60} i, j_{4} = \frac{8 2040 \times 2700 0 ^{2} + 1440 \times 2700 0 ^{2} 2}{60} - \frac{8 2040 \times 2700 0 ^{2} - 1440 \times 2700 0 ^{2} 2}{60} i

Alternative Form

j_{1} = - 192, j_{2} = 0, j_{3} \approx - 0.603914 + 0.250149 i, j_{4} \approx 0.603914 - 0.250149 i

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