Solve x4 + 16 = 0 . Express the roots in rectangular form .

Selena Cowan

Selena Cowan

Answered

2022-01-21

Solve x4 + 16 = 0 . Express the roots in rectangular form .

Answer & Explanation

KickAntitte06

KickAntitte06

Expert

2022-01-22Added 11 answers

The given expression is
x4 + 16 = 0
Adding and subtracting 8x2 , we get
x48x2+8x2+16=0
(x2+4)28x2=0
(x2+4)2(22x)2=0
(x2+4+22x)(x2+422x)=0
(a2b2=(a+b)(ab))
Solving the two quadratics separately.
(x2+4+22x)=0
By quadratic formula
x=22±84×42
=22±82
=22±22i2
=2±2i
Now , solving another quadratic equation, we get
(x2+422x)=0
By quadratic formula
x=22±84×42
=22±82
=22±22i2
=2±2i
Hence the roots of the given expression in rectangular form are
2+2i
22i
2+2i
22i

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