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How do we solve this?


Jiya Sharma

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This is best done using a diagram.

If arg(z)=0, it means the angle between the complex point (the vector leading to it) and the x-axis is 0. This implies that the point lies just on the x-axis (that represents real numbers) and the positive side (the angle is 0, not 180). There is no imaginary part to the number.

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Try to conceptualize it. An it is a concept number when drawn on an Argand's Diagram it will have an angle of 0.

So its just a line that coincides the real part, so there is no imaginary part.

This is just an idea of the solution.

Good Luck!

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If Arg(z) = 0 , show that z is real and positive.

Let the modulus be a real number r. This must be real by the definition of modulus.

Then, z = r cis(0) = r (cos(0) + i sin(0) ) = r (1 + 0i ) = r (1) = r.

As r is real, z is real.

We were just covering this in Math HL earlier this week! And if that's a real IB question the OP asked, that seems to be one of the easier complex number questions.

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