A few days ago
Solve the following quadratic equation: z^2+4z+(4+2i)=0?
It’s a question from a-level maths Complex Numbers chapter.
Top 2 Answers
A few days ago
Favorite Answer
z^2+4z+4 = -2i
(z+2)^2 = -2i
z = -2 ± √-2i = -2 ± √2√-i………….(*)
now, in the complex plane,
-i is at an angle 3π/2
so
√-i will be at angle 3π/4
ie
√-i = cos3π/4 + isin3π/4 = (-1 + i) /√2
substitute this in (*) gives
z = -2 ± √2√-i = -2 ± (-1 + i) = -1- i and -3 + i
.
1
A few days ago
two solutions
z = -1-i
and z = -3+i
solve the same way you would any other quadratic equation:
factor, complete the square, or use the quadratic formula.
surely you don’t need me to show you the tedious steps
what with you being an a-level maths student
(actually I used a different method to quickly find the solution)
0
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