Question

A complex number l z1 l = 13 and an angle ∅1 = 315°

Express z1 in rectangular form, as z1 = a +bi
Express a + bi in exact terms.
z1 =
​

Answer 1

The value of z1 is -10.6061 + 6.2349i.

Step-by-step explanation:

To express z1 in rectangular form, we need to determine the values of a and b in the equation z1 = a + bi. We can do this using the following formulas:

a = r * cos(θ)

b = r * sin(θ)

where r is the magnitude of z1 and θ is its angle in radians.

We are given that r = 13 and θ = 315°. Converting θ to radians, we get:

θ = 315° * (π/180°) = 5.5786 radians

Now we can plug in these values to the formulas:

a = 13 * cos(5.5786) = -10.6061

b = 13 * sin(5.5786) = 6.2349

Therefore, z1 can be expressed in rectangular form as:

z1 = -10.6061 + 6.2349i