Find the Complex Number z that Satisfies the Given Quadratic Equation :
Here we are going to see, how to find complex numbers that satisfies the given quadratic equation.
Question 1 :
Find two complex numbers z that satisfy the equation z2 + 4z + 6 = 0.
Solution :
z2 + 4z + 6 = 0
We may solve this quadratic equation using quadratic formula.
a = 1, b = 4 and c = 6
= [-b ± √(b2 - 4ac)] / 2a
= [-4 ± √(42 - 4(1)(6))] / 2(1)
= [-4 ± √(16 - 24)] / 2
= [-4 ± √-8] / 2
= 2[-2 ± √2i] / 2
= -2 ± √2i
Question 2 :
Find two complex numbers z that satisfy the equation 2z2 + 4z + 5 = 0.
Solution :
2z2 + 4z + 5 = 0
We may solve this quadratic equation using quadratic formula.
a = 2, b = 4 and c = 5
= [-b ± √(b2 - 4ac)] / 2a
= [-4 ± √(42 - 4(2)(5))] / 2(2)
= [-4 ± √(16 - 40)] / 4
= (-4 ± 2√6) / 4
= 2(-2 ± √6) / 4
= (-2 ± √6)/2
Question 3 :
Find a complex number whose square equals
5 + 12i
Solution :
(5 + 12i)2 = 52 + 2(5)(2i) + (2i)2
= 25 + 20i + 4i2
= 25 + 20i - 4
= 21 + 20i
Question 4 :
Find a complex number whose square equals
21 − 20i
Solution :
(21 - 20i)2 = 212 + 2(21)(20i) + (20i)2
= 441 + 840i + 400i2
= 441 + 840i - 400
= 41 + 840i
After having gone through the stuff given above, we hope that the students would have understood "Find the Complex Number z that Satisfies the Given Quadratic Equation".
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