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Find the complex number `z`satisfying `R e(z^2 0=0,|z|=sqrt(3.)` |
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Answer» `z = x +iy` or `z^(2) = x^(2) -y + 2ixy ` ` rArr Re(z^(2)) = x^(2) -y^(2)` Also, `|z| = sqrt(x^(2) + y^(2))` `rArr x^(2) -y^(2) = 0, x^(2) + y^(2) = 3` `rArr x^(2) = y^(2) = (3)/(2)` `rArr x =pm sqrt((3)/(2)), y = pm sqrt((3)/(2))` `rArr z = pm sqrt((3)/(2)) pm sqrt((3)/(2))i` Thus, there are four complex numbers. |
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