Q. 2 H5.0( 2 Votes )

# Solve the followi

Answer :

x2 – x + (1 + i) = 0

Given x2 – x + (1 + i) = 0

Recall that the roots of quadratic equation ax2 + bx + c = 0, where a ≠ 0, are given by Here, a = 1, b = –1 and c = (1 + i)     By substituting –1 = i2 in the above equation, we get  We can write 3 + 4i = 4 – 1 + 4i

3 + 4i = 4 + i2 + 4i [ i2 = –1]

3 + 4i = 22 + i2 + 2(2)(i)

3 + 4i = (2 + i)2 [ (a + b)2 = a2 + b2 + 2ab]

By using the result 3 + 4i = (2 + i)2, we get     [ i2 = –1]   x = i or 1 – i

Thus, the roots of the given equation are i and 1 – i.

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