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Byju's Answer
Standard XII
Mathematics
Modulus of a Complex Number
Find the four...
Question
Find the four roots of the equation
z
4
+
16
=
0
and them to factorize
z
4
+
16
into quadratic factors with real coefficients.
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Solution
z
4
+
16
=
0
z
4
=
−
16
z
4
=
16
i
2
z
4
=
±
4
i
4
i
=
2
(
2
i
)
=
2
(
1
+
2
i
−
1
)
=
2
(
1
+
2
i
+
i
2
)
=
2
(
1
+
i
)
2
So,
−
4
i
=
2
(
1
−
i
)
2
z
2
=
2
(
1
±
i
)
2
z
=
±
√
2
(
1
±
i
)
Four roots
=
√
2
(
1
+
i
)
,
√
2
(
1
−
i
)
,
−
√
2
(
1
+
i
)
&
−
√
2
(
1
−
i
)
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1
Similar questions
Q.
Solve the following quadratic equation by factorization, the roots are :
+
4
,
−
4
16
x
−
1
=
15
x
+
1
;
x
≠
0
,
−
1
Q.
Solving the following quadratic equation by factorization, the roots are :
2
,
−
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16
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x
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10
x
=
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Q.
If the following quadratic equation has two equal and real roots then find the value of
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:
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=
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Q.
Let the four roots of unity be
z
1
,
z
2
,
z
3
, and
z
4
, respectively.
Statement 1:
z
2
1
+
z
2
2
+
z
2
3
+
z
2
4
=
0
Statement 2:
z
1
+
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2
+
z
3
+
z
4
=
0
.
Q.
Solve the given quadratic equation by factorization method
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