Write z = 2(sqrt)2 + 2(sqrt)2i in polar form.
z = 4(sqrt)2 (cos pi/4 + i sin pi/4)
z = 4 (cos pi/4 + i sin pi/4)
z = 4 (cos 5pi/4 + i sin 5pi/4)
z = 4 (cos pi/2 + i sin pi/2)
Write z = -6i in polar form.
z = 6 cis 3pi/2
z = 6 cis pi/2
z = -6 cis 3pi/2
x = 6(sqrt)2 cis 3pi/2
I've tried figuring these two out but I need help
The full answers for the practice are:
B. z = 4(cos pi/4 + i sin pi/4)
A. z = 6 cis 3pi/2
D. z = 4sqrt3 - 4i
B. z = -2.25 - 1.1i
Whoops I'm wrong it's the first one
Yup, it is +6
the r value is considered positive, the direction will be take care
of by the angle.
Thank you for providing the correct answers!
To convert a complex number to polar form, we can use the following steps:
Step 1: Find the modulus (r):
The modulus of a complex number is the distance from the origin (0,0) to the point representing the complex number in the complex plane. It is calculated using the formula modulus (r) = sqrt(a^2 + b^2), where a is the real part and b is the imaginary part of the complex number.
Step 2: Find the argument (θ):
The argument of a complex number is the angle between the positive real axis and the line connecting the point representing the complex number to the origin (0,0) in the complex plane. It is calculated using the formula argument (θ) = arctan(b/a), where a is the real part and b is the imaginary part of the complex number.
Step 3: Write the complex number in polar form:
The polar form of a complex number is z = r(cosθ + isinθ), where r is the modulus and θ is the argument.
Now, let's apply these steps to the given complex numbers:
1. z = 2(sqrt(2)) + 2(sqrt(2))i:
First, let's find the modulus (r):
r = sqrt((2(sqrt(2)))^2 + (2(sqrt(2)))^2)
= sqrt(8 + 8)
= sqrt(16)
= 4
Next, let's find the argument (θ):
θ = arctan((2(sqrt(2)))/(2(sqrt(2))))
= arctan(1)
= π/4
Now, we can write the complex number in polar form:
z = 4(cos(π/4) + isin(π/4))
2. z = -6i:
First, let's find the modulus (r):
r = sqrt(0 + (-6)^2)
= sqrt(36)
= 6
Next, let's find the argument (θ):
θ = arctan((-6)/0)
= π/2
Now, we can write the complex number in polar form:
z = 6(cos(π/2) + isin(π/2))
So, the polar forms of the given complex numbers are:
1. z = 4(cos(π/4) + isin(π/4))
2. z = 6(cos(π/2) + isin(π/2))
The third one: z = -6 cis 3pi/2
z = 2√2 + 2√2 i
r = √(8+8) = 4
tanØ = 2√2/(2√2) = 1
Ø = π/4
z = 4(cosπ/4 + i sinπ/4) or 4cisπ/4 , if you learned that abbreviation
for z = -6i
consider it as z = 0 - 6i and proceed as before
from the graph in the Argand plane , it can be seen that the angle is 3π/2
which of the answer choices would apply ?