Express the following complex numbers in the form re (a) 4 3i (b) -2 -i

(a) 5 {Cos 37° + i Sin 37°}

(b) 2.24 {Cos 206.6° + i Sin 206.6°}

Explanation:

(a) 4 + 3 i

Here it is written in standard form

Z = r (Cosθ + i Sinθ)

By comparison

r cosθ = 4

r sinθ = 3

Squarring both sides and then add

r = 5

By dividing

tanθ = 0.75

θ = 37°

So, it is written as 5 {Cos 37° + i Sin 37°}

(b) -2 - i

Here it is written in standard form

Z = r (Cosθ + i Sinθ)

By comparison

r cosθ = -2

r sinθ = - 1

Squarring both sides and then add

r = 2.24

By dividing

tanθ = 0.5

θ = 206.6°

So, it is written as 2.24 {Cos 206.6° + i Sin 206.6°}

answer: the metamorphic rocks are formed when they are exposed to high pressure and high temperatures. this happens when one of the earth's plates comes in contact with the other plate by traveling in opposite directions, straight into each other or slipping under one another. the friction that is caused by this activity results in   melting of rocks and when it cools they are known as metamorphic rocks. this process needs a controlled amount of pressure and temperature otherwise it may turn into magma.