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Question
If z1 and z2 are complex numbers such that z1 + z2 is a real number, then z2 = ______.
Solution
If z1 and z2 are complex numbers such that z1 + z2 is a real number, then z2 = `underlinebb(barz_1)`.
Explanation:
Let z1 = x1 + iy1 and z2 = x2 + iy2
z1 + z2 = (x1 + iy2) + (x2 + iy2)
z1 + z2 = (x1 + x2) + (y1 + y2)i
If z1 + z2 is real then,
y1 + y2 = 0
⇒ y1 = –y2
∴ z2 = x2 – iy1
z2 = x1 – iy1 ......(When x1 = x2)
So z2 = `barz_1`
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