Find the modulus and amplitude of = 1 +
Answers
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Answer:
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Step-by-step explanation:
Answer:
Modulus - |Z|=\sqrt 2∣Z∣=
2
Amplitude - \theta=\frac{\pi}{4}θ=
4
π
Step-by-step explanation:
To find : The modulus and amplitude of 1+i ?
Solution :
If z=a+ib is any complex number such that a∈R, b∈R then the
Modulus of complex number, |Z| is given by |Z|=\sqrt{a^2+b^2}∣Z∣=
a
2
+b
2
Amplitude of the complex number, θ is given by, \theta= \tan^{-1}(\frac{b}{a})θ=tan
−1
(
a
b
)
On comparing, a=1 and b=1
|Z|=\sqrt{a^2+b^2}=\sqrt{1^2+1^2}=\sqrt{2}∣Z∣=
a
2
+b
2
=
1
2
+1
2
=
2
\theta=\tan^{-1}(\frac{b}{a})=\tan^{-1}(\frac{1}{1})=\tan^{-1}\tan(\frac{\pi}{4})θ=tan
−1
(
a
b
)=tan
−1
(
1
1
)=tan
−1
tan(
4
π
)
\theta=\frac{\pi}{4}θ=
4
π
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Answer:
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