To solve this quadratic equation, we can first rewrite it in standard form (ax^2 + bx + c = 0) by combining like terms:
z^2 + 4z + 5 = 0
Next, we can solve for z by factoring or using the quadratic formula. In this case, the quadratic formula will be used:
z = (-b ± √(b^2 - 4ac)) / 2a
In the equation z^2 + 4z + 5 = 0,
a = 1, b = 4, c = 5
Plugging these values into the formula:
z = (-4 ± √(4^2 - 415)) / 2*1z = (-4 ± √(16 - 20)) / 2z = (-4 ± √(-4)) / 2z = (-4 ± 2i) / 2z = -2 ± i
Therefore, the solutions to the quadratic equation z^2 + 4z + 5 = 0 are z = -2 + i and z = -2 - i.
To solve this quadratic equation, we can first rewrite it in standard form (ax^2 + bx + c = 0) by combining like terms:
z^2 + 4z + 5 = 0
Next, we can solve for z by factoring or using the quadratic formula. In this case, the quadratic formula will be used:
z = (-b ± √(b^2 - 4ac)) / 2a
In the equation z^2 + 4z + 5 = 0,
a = 1, b = 4, c = 5
Plugging these values into the formula:
z = (-4 ± √(4^2 - 415)) / 2*1
z = (-4 ± √(16 - 20)) / 2
z = (-4 ± √(-4)) / 2
z = (-4 ± 2i) / 2
z = -2 ± i
Therefore, the solutions to the quadratic equation z^2 + 4z + 5 = 0 are z = -2 + i and z = -2 - i.