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1

### IIT-JEE 1990

Subjective
Let $${z_1}$$ = 10 + 6i and $${z_2}$$ = 4 + 6i. If Z is any complex number such that the argument of $${{(z - {z_1})} \over {(z - {z_2})}}\,is{\pi \over 4}$$ , then prove that $$\left| {z - 7 - 9i} \right| = 3\sqrt 2$$.

Solve it.
2

### IIT-JEE 1986

Subjective
Show that the area of the triangle on the Argand diagram formed by the complex numbers z, iz and z + iz is $${1 \over 2}\,{\left| z \right|^2}$$ .

Solve it.
3

### IIT-JEE 1984

Subjective
If 1, $${{a_1}}$$, $${{a_2}}$$......,$${a_{n - 1}}$$ are the n roots of unity, then show that (1- $${{a_1}}$$) (1- $${{a_2}}$$) (1- $${{a_3}}$$) ....$$(1 - \,a{ - _{n - 1}}) = n$$

Solve it.
4

### IIT-JEE 1983

Subjective
Prove that the complex numbers $${{z_1}}$$, $${{z_2}}$$ and the origin form an equilateral triangle only if $$z_1^2 + z_2^2 - {z_1}\,{z_2} = 0$$.

Solve it.

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Class 12