How do I use the modulus and argument to square (1+i)?

1 Answer
Daniel L.
Apr 27, 2018

You should use the de Moivre's Theorem. See explanation.

Explanation:

For any complex number z given in trigonometric form (having modulus |z| and argument varphi) we can calculate any natural power using the formula:

z^n=|z|^n*(cosnvarphi+i*sinnvarphi)

Here we get:

|z|=sqrt(1^2+1^2)=sqrt(2)

cosvarphi=(Re(z))/|z|=1/sqrt(2)=sqrt(2)/2=> varphi=45^o

Now we can calculate the square:

z^2=|z|^2*(cos(2*45)+isin(2*45))=

=2*(cos90+isin90)=2*(0+1i)=2i

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