Prove that the cross ratio of four complex numbers z1, z2, z3, z4 is real if...

Prove that the cross ratio of four complex numbers z1, z2, z3, z4 is real if and only if the points z1, z2, z3, z4 lie on a line or a circle. Then, compute the cross ratio of 1+√ 3, 1−3i, −1 − i and 1 + i and determine whether they lie on a line, a circle, or neither.

Expert Solution

Colby Messinger answered 2 years ago

(a) Let U={(z1, z2, z3, z4, z5)∈C: 6z1=z2, z3+ 2z4+ 3z5= 0}. Check if U is...

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(a) look at these the complex numbers z1 = − √ 3 + i and z2...

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given z1=2+j3, z2=7+j1, z3=5+j9. find the value of the following expressions in both coordinate and Euler forms. a) z1z2,z2z3,z3z3(dash on top z),(z1+z3)z2 b) z1/z2,z2/z3,z3(dash on to[ z)/z3,(z1+z2)/z3.

1. How many complex numbers z are there such that z3 = 1? 2. Translate x(t)...

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