Complex Number (Graphical Representation) Exercise 1: Represent π§ = β3 + 4π in an Argand diagram and find its modulus and argument. π°π(π)
Modulus: π =
=π
Argument: πππ π =
πΉπ(π)
= πππ. ππππΒ° ~mys2020~
4
Complex Number (Graphical Representation) Exercise 2: Represent π§ = β6 β 5π in an Argand diagram and find its modulus and argument. Modulus: π =
= ππ
Argument: πππ π =
= πππ. ππππΒ° ~mys2020~
5
Complex Number (Graphical Representation) Exercise 3: Represent π§ = 4 β 7π in an Argand diagram and find its modulus and argument.
Modulus: π =
= ππ
Argument: πππ π =
= πππ. ππππΒ° ~mys2020~
6
Complex Number (Graphical Representation) Exercise 4: Represent π§ = 5 + 9π in an Argand diagram and find its modulus and argument.
Modulus: π =
= πππ
Argument: πππ π =
= ππ. ππππΒ° ~mys2020~
7
Complex Number (Graphical Representation) Exercise 5: Represent π§ = β8 + 4π in an Argand diagram and find its modulus and argument. Modulus: π =
= ππ
Argument: πππ π =
= πππ. ππππΒ° ~mys2020~
8
Complex Number (Graphical Representation) Exercise 6: Given π§1 = 5 + 3π and π§2 = 4 β 6π, represent each of the following in an Argand diagram and find its modulus and argument. a.
Complex Number (Polar form, Exponential form and Trigonometric form) Example: Convert z = 3 + 5π into trigonometric form, polar form and exponential form. Step 1: Find the values of modulus and argument 5 3 = ππ. ππππΒ°
π = 32 + 52 = ππ
π = tanβ1
Step 2: Plot the complex number in an Argand diagram π°π(π) π
π = π + ππ
π½ = ππ. ππππΒ° π
πΉπ(π) ~mys2020~
12
Complex Number (Polar form, Exponential form and Trigonometric form) Step 3: Substitute the values of π and π into the formulas. Trigonometric form
π§ = π cos π + π sin π = 34 cos 59.0362 + π sin 59.0362 Polar form π§ = πβ πΒ° = 34β 59.0362Β° Exponential form π0 = 59.0362 Γ = 1.0304 πππ
Complex Number (Polar form, Exponential form and Trigonometric form) Exercise 1: Convert z = 4 + 6π into trigonometric form, polar form and exponential form.
~mys2020~
= ππ cos ππ. ππππΒ° + π sin ππ. ππππΒ° = ππβ ππ. ππππΒ° = ππππ.πππππ 14
Complex Number (Polar form, Exponential form and Trigonometric form) Exercise 2: Convert π§ = 25β 48Β° into trigonometric form, cartesian form and exponential form.
= ππ cos ππΒ° + π sin ππΒ° = ππ. ππππ + ππ. πππππ = ππππ.πππππ ~mys2020~
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Complex Number (Polar form, Exponential form and Trigonometric form) Exercise 3: Given π§1 = 12β 45Β° , π§2 = 24 cos 10Β° + π sin 10Β° and π§3 = 14π 0.342π . Calculate: a.