We were given 10 questions to do, and i cant do one. it is:
Z^2 + 4z + 19 = 0. And the question says to write your soloution in the form z = a + bi, giving exact values for a and b.
any help would be appreciated!
Z^2 + 4z + 19 = 0. And the question says to write your soloution in the form z = a + bi, giving exact values for a and b.
any help would be appreciated!
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z^2+4z+19 = 0
Quadratic Formula: x = -b+-√(b^2-4ac) / 2a
In this problem: a=1, b=4, and c=19.
z = -(4)+-√((4)^2-4(1)(19)) / 2(1)
z = -4+-√(16-76) / 2
z = -4+-√-60 / 2
z = -4+-√4√-15 / 2
z = -4+-2√-15 / 2
z = 2(-2+-√-15) / 2
z = -2+-√-15
z = -2+-√15√-1
z = -2+-(√15)i
Answer: z=-2+(√15)i or z=-2-(√15)i
Quadratic Formula: x = -b+-√(b^2-4ac) / 2a
In this problem: a=1, b=4, and c=19.
z = -(4)+-√((4)^2-4(1)(19)) / 2(1)
z = -4+-√(16-76) / 2
z = -4+-√-60 / 2
z = -4+-√4√-15 / 2
z = -4+-2√-15 / 2
z = 2(-2+-√-15) / 2
z = -2+-√-15
z = -2+-√15√-1
z = -2+-(√15)i
Answer: z=-2+(√15)i or z=-2-(√15)i
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(z+2)^2 + 15 = (z+2 + i sqrt15)(z+2 - i sqrt15) = 0 --->z = ..