Solve x^2 169=0 13i - ScanMath

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Type your math problem... x^2 169=0 13i

Question

Solve the equation

x_{1} = \frac{26}{26} + \frac{26}{26} i x_{2} = - \frac{26}{26} - \frac{26}{26} i

Alternative Form

x_{1} \approx 0.196116 + 0.196116 i x_{2} \approx - 0.196116 - 0.196116 i

Evaluate

x^{2} \times 169 = 13 i

Use the commutative property to reorder the terms

169 x^{2} = 13 i

Divide both sides

\frac{169 x ^{2}}{169} = \frac{13 i}{169}

Divide the numbers

x^{2} = \frac{13 i}{169}

Divide the numbers

More Steps

x^{2} = \frac{1}{13} i

Simplify

x = \frac{1}{13} i

Rewrite the complex number in polar form

More Steps

x = \frac{1}{13} (cos (\frac{π}{2}) + i sin (\frac{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})

x = \frac{1}{13} \times (cos (\frac{\frac{π}{2} + 2 kπ}{2}) + i sin (\frac{\frac{π}{2} + 2 kπ}{2}))

Simplify

x = \frac{13}{13} (cos (\frac{\frac{π}{2} + 2 kπ}{2}) + i sin (\frac{\frac{π}{2} + 2 kπ}{2}))

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

x_{1} = \frac{13}{13} (cos (\frac{\frac{π}{2} + 2 \times 0 \times π}{2}) + i sin (\frac{\frac{π}{2} + 2 \times 0 \times π}{2})) x_{2} = \frac{13}{13} (cos (\frac{\frac{π}{2} + 2 \times 1 \times π}{2}) + i sin (\frac{\frac{π}{2} + 2 \times 1 \times π}{2}))

Calculate

More Steps

x_{1} = \frac{13}{13} (cos (\frac{π}{4}) + i sin (\frac{π}{4})) x_{2} = \frac{13}{13} (cos (\frac{\frac{π}{2} + 2 \times 1 \times π}{2}) + i sin (\frac{\frac{π}{2} + 2 \times 1 \times π}{2}))

Calculate

More Steps

x_{1} = \frac{13}{13} (cos (\frac{π}{4}) + i sin (\frac{π}{4})) x_{2} = \frac{13}{13} (cos (\frac{5 π}{4}) + i sin (\frac{5 π}{4}))

Solution

x_{1} = \frac{26}{26} + \frac{26}{26} i x_{2} = - \frac{26}{26} - \frac{26}{26} i

Alternative Form

x_{1} \approx 0.196116 + 0.196116 i x_{2} \approx - 0.196116 - 0.196116 i

Show Solution