If the moduli of two complex numbers are less | vedclass

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(D) Let the two complex numbers be $z_1$ and $z_2$ such that $|z_1| < 1$ and $|z_2| < 1$. By the triangle inequality,we have $|z_1 + z_2| \leq |z_1| +

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(D) Let the two complex numbers be $z_1$ and $z_2$ such that $|z_1| By the triangle inequality,we have $|z_1 + z_2| \leq |z_1| + |z_2|$. Since $|z_1| This implies $|z_1 + z_2| However,the value of $|z_1 + z_2|$ can be less than,greater than,or equal to $1$. For example,if $z_1 = 0.1$ and $z_2 = 0.1$,then $|z_1 + z_2| = 0.2 If $z_1 = 0.8$ and $z_2 = 0.8$,then $|z_1 + z_2| = 1.6 > 1$. If $z_1 = 0.5$ and $z_2 = 0.5$,then $|z_1 + z_2| = 1$. Thus,the modulus of the sum can be any value in the interval $[0, 2)$.

If the moduli of two complex numbers are less than unity,then the modulus of the sum of these complex numbers is:

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