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Let z=a+ 4i and w=a+ 7i where aR. Without using a calculator, (a) determine zw, and hence, all values of a such that zw is

Let z=a+ 4i and w=a+ 7i where aR. Without using a calculator,

(a) determine zw, and hence, all values of a such that zw is purely imaginary;

(b) determine 1/z+iw in cartesian form.

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