Question

find modulus and amplitude of the complex number z= 1+I
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Answer 1

Here is your answer fully solved...

hope it helps

Answer 2

The value of modulus and amplitude of  the complex number z= 1+i  are $\sqrt{2}$ and $\frac{\pi }{4}$ respectively.

Step-by-step explanation:

Given:

Complex number z= 1+i

To Find:

The value of modulus and amplitude of the complex number z= 1+i.

Formula Used:

Let  the complex number z= p+iq such that p∈R, q∈R

Modulus of complex number |Z|  =$\sqrt{p^{2} +q^{2} }$    ----------- Formula no.01

Amplitude of the complex number  θ  $=tan^{-1}(\frac{q}{p} )$    -----Formula no.02.

Solution:

As given-Complex number z= 1+i

Comparing with complex number z= p+iq

p=1 and q=1

Applying formula no.01.

Modulus of complex number |Z|  =$\sqrt{p^{2} +q^{2} }$

                                                      $=\sqrt{1^{2} +1^{2} }$

                                                      $=\sqrt{1+1}$   = $\sqrt{2}$

Applying formula no.02.

Amplitude of the complex number  θ  $=tan^{-1}(\frac{q}{p} )$

                                                                $=tan^{-1}(\frac{1}{1} )$

                                                                $=tan^{-1}(1)$

                                                                 $=\frac{\pi }{4}$

Thus,the value of modulus and amplitude of  the complex number z= 1+i  are $\sqrt{2}$ and $\frac{\pi }{4}$ respectively.

PROJECT CODE #SPJ3