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4. If z=x+yi and , prove that

By solving the equation for or otherwise, express each root of the equation in the form x+yi.

5a. Express the complex numbers 1+i and 1-i in the form , where r is the modulus and the argument of .

5b. Given that and , find, in the form a+bi, the complex number z such that .

Find the modulus and argument of z, giving your answer for arg z in the range , correct to 3 decimal places.

Answers:

4.

5a. ,

5b.