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Chapter 2: Q31MP (page 81)

Show that if a sequence of complex numbers tends to zero, then the sequence of absolute values tends to zero too, and vice versa. Hintan+ibn鈫�0means an鈫�0andbn鈫�0.

Short Answer

Expert verified

It has been proved thatan+ibn鈫�0 means

Step by step solution

01

Given Information.

It has been given that the complex numbers tends to zero.

02

Meaning of rectangular form.

Represent the complex number in rectangular form means writing the given complex number in the form of x+iyin which x is the real part and y is the imaginary part.

03

Solve the series.

Assume a sequence of complex number.

S=鈭�CnS=C1+C2+C3+鈰�

A complex number has a real and an imaginary part.

S=鈭�CnS=鈭�an+ibnS=鈭�an+i鈭�bn

If tends to be zero thentends to be zero and this is only possible when must be zero.

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