Question Type 3: Calculating modulus of complex numbers Exercises

Compute the modulus of the complex number $5+6i$.

Express $|x+yi|^2$ in terms of $x$ and $y$, then compute $|3+4i|^2$.

Verify that $|z^2|=|z|^2$ for $z=-1+i$, and compute its value.

Given $z=1+i$ and $w=2+2i$, verify that $|zw|=|z|\,|w|$.

Compute the sum $|3+4i|+|4+3i|$.

Calculate the modulus of $1-\sqrt{3}\,i$.

Determine whether the point $6-2i$ lies inside, on, or outside the circle defined by $|z-(1+i)|=5$.

Find the modulus of the quotient $\frac{3+4i}{1-2i}$.

Compute the modulus of the product $(1+2i)(2-3i)$.

Find the modulus of $2-2i$.

Compute the modulus of the complex number $-3+4i$.