Solve 5c^3i=90 - ScanMath

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Question

Solve the equation

c_{1} = 318 \times i c_{2} = - \frac{3 6 12}{2} - \frac{3 18}{2} i c_{3} = \frac{3 6 12}{2} - \frac{3 18}{2} i

Alternative Form

c_{1} \approx 2.620741 i c_{2} \approx - 2.269629 - 1.310371 i c_{3} \approx 2.269629 - 1.310371 i

Evaluate

5 c^{3} i = 90

Multiply the numbers

5 i c^{3} = 90

Divide both sides

\frac{5 i c ^{3}}{5 i} = \frac{90}{5 i}

Divide the numbers

c^{3} = \frac{90}{5 i}

Divide the numbers

More Steps

c^{3} = - 18 i

Simplify

c = 3 - 18 i

Rewrite the complex number in polar form

More Steps

c = 3 18 (cos (\frac{3 π}{2}) + i sin (\frac{3 π}{2}))

Calculate the nth roots of a complex r (cos (θ) + i \times sin (θ),using n z = n r (cos \frac{θ + 2 kπ}{n} + i sin \frac{θ + 2 kπ}{n})

c = 318 \times (cos (\frac{\frac{3 π}{2} + 2 kπ}{3}) + i sin (\frac{\frac{3 π}{2} + 2 kπ}{3}))

Since n = 3,substitute k = 0, 1, 2 into the expression

c_{1} = 318 \times (cos (\frac{\frac{3 π}{2} + 2 \times 0 \times π}{3}) + i sin (\frac{\frac{3 π}{2} + 2 \times 0 \times π}{3})) c_{2} = 318 \times (cos (\frac{\frac{3 π}{2} + 2 \times 1 \times π}{3}) + i sin (\frac{\frac{3 π}{2} + 2 \times 1 \times π}{3})) c_{3} = 318 \times (cos (\frac{\frac{3 π}{2} + 2 \times 2 π}{3}) + i sin (\frac{\frac{3 π}{2} + 2 \times 2 π}{3}))

Calculate

More Steps

c_{1} = 318 \times (cos (\frac{π}{2}) + i sin (\frac{π}{2})) c_{2} = 318 \times (cos (\frac{\frac{3 π}{2} + 2 \times 1 \times π}{3}) + i sin (\frac{\frac{3 π}{2} + 2 \times 1 \times π}{3})) c_{3} = 318 \times (cos (\frac{\frac{3 π}{2} + 2 \times 2 π}{3}) + i sin (\frac{\frac{3 π}{2} + 2 \times 2 π}{3}))

Calculate

More Steps

c_{1} = 318 \times (cos (\frac{π}{2}) + i sin (\frac{π}{2})) c_{2} = 318 \times (cos (\frac{7 π}{6}) + i sin (\frac{7 π}{6})) c_{3} = 318 \times (cos (\frac{\frac{3 π}{2} + 2 \times 2 π}{3}) + i sin (\frac{\frac{3 π}{2} + 2 \times 2 π}{3}))

Calculate

More Steps

c_{1} = 318 \times (cos (\frac{π}{2}) + i sin (\frac{π}{2})) c_{2} = 318 \times (cos (\frac{7 π}{6}) + i sin (\frac{7 π}{6})) c_{3} = 318 \times (cos (\frac{11 π}{6}) + i sin (\frac{11 π}{6}))

Solution

c_{1} = 318 \times i c_{2} = - \frac{3 6 12}{2} - \frac{3 18}{2} i c_{3} = \frac{3 6 12}{2} - \frac{3 18}{2} i

Alternative Form

c_{1} \approx 2.620741 i c_{2} \approx - 2.269629 - 1.310371 i c_{3} \approx 2.269629 - 1.310371 i

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