Solve sqrt(52i) - ScanMath

Question

Simplify the expression

213 \times (cos (\frac{π}{4}) + i sin (\frac{π}{4})) 213 \times (cos (\frac{5 π}{4}) + i sin (\frac{5 π}{4}))

Alternative Form

26 + 26 \times i - 26 - 26 \times i

Evaluate

52 i

Rewrite the complex number in polar form

More Steps

52 (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})

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

Simplify

213 \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

213 \times (cos (\frac{\frac{π}{2} + 2 \times 0 \times π}{2}) + i sin (\frac{\frac{π}{2} + 2 \times 0 \times π}{2})) 213 \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

213 \times (cos (\frac{π}{4}) + i sin (\frac{π}{4})) 213 \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

213 \times (cos (\frac{π}{4}) + i sin (\frac{π}{4})) 213 \times (cos (\frac{5 π}{4}) + i sin (\frac{5 π}{4}))

Alternative Form

26 + 26 \times i - 26 - 26 \times i

Show Solution