Can help me to solve this?
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.
For a complex number , to convert to polar form , you need to know the following:
(subject to correction, since inverse tangent only gives angles in .
For 1 + i (or 1 + 1i),
For 1 - i (or 1 - 1i),
As HallsofIvy has shown, & are coterminal angles. I added above because I wanted an angle that was in the interval .
As far as I'm concerned my answers match what you originally posted.
The last two numbers, , are the modulus and argument, respectively, of my answer5a. ,
.
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