Solve sqrt(512i) - ScanMath

Question

Simplify the expression

162 \times (cos (\frac{π}{4}) + i sin (\frac{π}{4})) 162 \times (cos (\frac{5 π}{4}) + i sin (\frac{5 π}{4}))

Alternative Form

16 + 16 i - 16 - 16 i

Evaluate

512 i

Rewrite the complex number in polar form

More Steps

512 (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})

512 \times (cos (\frac{\frac{π}{2} + 2 kπ}{2}) + i sin (\frac{\frac{π}{2} + 2 kπ}{2}))

Simplify

162 \times (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

162 \times (cos (\frac{\frac{π}{2} + 2 \times 0 \times π}{2}) + i sin (\frac{\frac{π}{2} + 2 \times 0 \times π}{2})) 162 \times (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

162 \times (cos (\frac{π}{4}) + i sin (\frac{π}{4})) 162 \times (cos (\frac{\frac{π}{2} + 2 \times 1 \times π}{2}) + i sin (\frac{\frac{π}{2} + 2 \times 1 \times π}{2}))

Solution

More Steps

162 \times (cos (\frac{π}{4}) + i sin (\frac{π}{4})) 162 \times (cos (\frac{5 π}{4}) + i sin (\frac{5 π}{4}))

Alternative Form

16 + 16 i - 16 - 16 i

Show Solution