Solved Mathematics Questions For University Freshers

Question:​​ Define Amplitude and Polar form, thus determine the amplitude and polar form of the complex number

ƶ ​​​​ =2​​ +​​ 2i

Answers

Amplitude​​ is​​ the angle between the real part and the imaginary part of a complex number, it is also known as principal argument (θ) it can be in radian or degree.

 ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​​​ 

θ​​ = tan-1(yx)​​ =​​ ​​ tan-1​​ (22)​​ =​​ tan-1​​ 1​​ =45 ​​ ​​ ​​ ​​ ​​​​ ​​ 

θ= 450 ​​​​ ​​ or ​​ π4​​ 

Polar form​​ is a mathematical representation​​ that connects modulus/magnitude (ṝ) to the principal argument (Amplitude) in a complex number

Polar form​​ =​​ r(Cos​​ θ​​ +​​ i​​ Sin​​ θ)​​ =​​ r cis​​ θ

Where r ​​ =​​ 22+22 ​​ ​​​​ =​​ 22

Polar form  ​​​​ = ​​​​ 22 ​​​​ cis​​ π4