Question

Review the graph of complex number z. Plotted at (5,-5)

What is the polar form of z?
A. 5(cos(pi/4)+isin(pi/4))
B. 5sqrt2(cos(pi/4)+isin(pi/4))
C. 5(cos(-pi/4)+isin(-pi/4))
D. 5sqrt2(cos(-pi/4)+isin(-pi/4))

Answer 1

D. 5sqrt2(cos(-pi/4)+isin(-pi/4))

Explanation:

The polar form of a complex number z is given by r(cos(θ)+isin(θ)), where r is the magnitude of z and θ is the argument of z.

The magnitude r can be calculated as the square root of the sum of the squares of the real and imaginary parts of z.

In this case, r = sqrt(5^2 + (-5)^2) = 5sqrt(2).

The argument θ can be calculated as the arctangent of the imaginary part divided by the real part.

In this case, θ = arctan(-5/5) = -pi/4.

So, the polar form of z is 5sqrt(2)(cos(-pi/4)+isin(-pi/4)).