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Question Number 19688 by Tinkutara last updated on 14/Aug/17

The vertices of a square are z_{1}, z_{2}, z_{3}

and z_{4} taken in the anticlockwise order,

then z_{3} =

(1) - {i z}_{1} + (1 + i) z_{2}

(2) {i z}_{1} + (1 + i) z_{2}

(3) z_{1} + (1 + i) z_{2}

(4) (1 + i) z_{1} + z_{2}

Answered by ajfour last updated on 14/Aug/17

z_{3} = z_{1} + (z_{2} - z_{1}) e^{i π / 4} \times \sqrt{2}

= z_{1} + (z_{2} - z_{1}) (1 + i)

z_{3} = - {iz}_{1} + (1 + i) z_{2} . (1)

Commented by Tinkutara last updated on 15/Aug/17

Thank you very much Sir!