show that root 3 upon 2 plus iota upon 2 cube is equal to iota
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Answer:
Answer:
a²=b and b²=a proved.
Step-by-step explanation:
We are given that,
a=\frac{-1+i\sqrt{3}}{2}a=
2
−1+i
3
..... (1)
and, b= \frac{-1-i\sqrt{3}}{2}b=
2
−1−i
3
..... (2)
We have to prove that, a²=b and b²=a
Now, from (1) {Squaring both sides of (1)},
a²=\frac{1-3-i(2\sqrt{3})}{4}
4
1−3−i(2
3
)
⇒ a²= \frac{-2-i(2\sqrt{3})}{4}
4
−2−i(2
3
)
⇒ a²= \frac{-1-i\sqrt{3}}{2}
2
−1−i
3
⇒ a²= b {From equation (2)} (Proved)
Again, from (2) {Squaring both sides of (2)},
b²= \frac{1-3+i(2\sqrt{3})}{4}
4
1−3+i(2
3
)
⇒ b²= \frac{-2+i(2\sqrt{3})}{4}
4
−2+i(2
3
)
⇒ b²= \frac{-1+i\sqrt{3}}{2}
2
−1+i
3
⇒ b²= a {From equation (2)} (Hence, proved).
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