Represent the complex number graphically and find the standard form of the number 5(cos 135* + isin 135*)
To represent a complex number graphically, we can use the Cartesian coordinate system. In this system, the real part of the complex number represents the x-axis, and the imaginary part represents the y-axis.
The standard form of a complex number is of the form a + bi, where a is the real part and b is the imaginary part.
In the given complex number, 5(cos 135° + isin 135°), the real part is 5cos 135° and the imaginary part is 5sin 135°.
To find the standard form, we can use the trigonometric identities: cos θ = cos(-θ) and sin θ = -sin(-θ).
cos 135° = cos(-225°) = -cos 45° = -1/√2
sin 135° = -sin(-225°) = sin 45° = 1/√2
Therefore, the standard form of the given complex number is:
5(cos 135° + isin 135°) = 5(-1/√2 + i/√2) = (-5/√2) + (5/√2)i.