FIND COMPLEX NUMBERS Z 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

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