Que 8. (aFind the square root of 8-15

1.	Que 8. (aFind the square root of 8-15
Answer» Let sqrt(8 + 5i) = a + ib where a is real part and b is imaginary part. squaring both sides, 8 - 5i = a² + (ib)² + 2a.ib ⇒8 - 5i = a² - b² + i(2ab) Compare both sides , a² - b² = 8 and 2ab = -5 (a² + b²)² = (a² - b²)² + 4a²b² = 8² + (-5)² = 64 + 25 = 89 a² + b² = ±√89 Now, a² - b² + a² + b² = 8 ± √89 2a² = 8 ± √89 ⇒a² = 4 ± √(89/4) a = √(4 + √(89/4)) = 2.95 find b=0.84 Then, a and b put in a + ib a + ib is square root of 8 -5ihence, 2.95+0.84i

Answer»

Let sqrt(8 + 5i) = a + ib where a is real part and b is imaginary part.

squaring both sides, 8 - 5i = a² + (ib)² + 2a.ib ⇒8 - 5i = a² - b² + i(2ab)

Compare both sides , a² - b² = 8 and 2ab = -5 (a² + b²)² = (a² - b²)² + 4a²b² = 8² + (-5)² = 64 + 25 = 89 a² + b² = ±√89

Now, a² - b² + a² + b² = 8 ± √89 2a² = 8 ± √89 ⇒a² = 4 ± √(89/4) a = √(4 + √(89/4)) = 2.95 find b=0.84

Then, a and b put in a + ib a + ib is square root of 8 -5ihence, 2.95+0.84i

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