If z₁=a+ib, z₂=c+id with |z₁|=|z₂|=1 and Re(z₁ z₂)=0, then w₁=a+ic, w₂=b+id satisfy (a) |w₁|=1 (b) |w₂|=1 (c) Re(w₁ w₂)=0 (d) none of these

Correct answer: (a) |w₁|=1 The condition forces z₂ to be z₁ rotated by ±90^°; then |w₁|=|w₂|=1 and Re(w₁ w₂)=0 all hold. JEE Advanced 1985 · Complex Numbers — verified solution by the Vidaara Team.

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[JEE Advanced 1985] if z 1 a ib z 2 c id with z 1 z 2

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If $z_1=a+ib,\ z_2=c+id$ with $|z_1|=|z_2|=1$ and $\operatorname{Re}(z_1\bar z_2)=0$, then $w_1=a+ic,\ w_2=b+id$ satisfy

(a) $|w_1|=1$
(b) $|w_2|=1$
(c) $\operatorname{Re}(w_1\bar w_2)=0$
(d) none of these

1 Answer

VAVidaara Admin ✓ Vidaara Team ✓ Accepted · 2d ago ▲ 0

Correct answer: (a) $|w_1|=1$

The condition forces $z_2$ to be $z_1$ rotated by $\pm90^\circ$; then $|w_1|=|w_2|=1$ and $\operatorname{Re}(w_1\bar w_2)=0$ all hold.

JEE Advanced 1985 · Complex Numbers — verified solution by the Vidaara Team.

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