Finding modulus and argument of complex number (x+iy)

Draw argand diagram

Modulus=|z|= length of the line

So |z|=(x2+y2)0.5

Argument=Angle between real (x axis) and line

so arg(z)=arctan(y/x)

Related Further Mathematics A Level answers

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The rectangular hyperbola H has parametric equations: x = 4t, y = 4/t where t is not = 0. The points P and Q on this hyperbola have parameters t = 1/4 and t = 2 respectively. The line l passes through the origin O and is perpendicular to the line PQ.


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Find the complex number z such that 5iz+3z* +16 = 8i. Give your answer in the form a + bi, where a and b are real numbers.


Why is the argument of a+bi equal to arctan(b/a)?


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