Question

What is the polar form of z?

5 (cosine (StartFraction pi Over 4 EndFraction) + I sine (StartFraction pi Over 4 EndFraction) )
5 StartRoot 2 EndRoot (cosine (StartFraction pi Over 4 EndFraction) + I sine (StartFraction pi Over 4 EndFraction) )
5 (cosine (negative StartFraction pi Over 4 EndFraction) + I sine (negative StartFraction pi Over 4 EndFraction) )
5 StartRoot 2 EndRoot (cosine (negative StartFraction pi Over 4 EndFraction) + I sine (negative StartFraction pi Over 4 EndFraction) )

Answer 1

Explanation:

To express a complex number in polar form, we use the magnitude (or modulus) and argument (or angle) of the complex number.

For the complex number 5(cos(pi/4) + i*sin(pi/4)), the magnitude is 5, and the argument is pi/4.

Therefore, the polar form of the complex number is:

5 * (cos(pi/4) + i*sin(pi/4))

Similarly, for the complex number 5√2(cos(pi/4) + i*sin(pi/4)), the magnitude is 5√2, and the argument is pi/4.

Therefore, the polar form of the complex number is:

5√2 * (cos(pi/4) + i*sin(pi/4))

For the complex number 5(cos(-pi/4) + i*sin(-pi/4)), the magnitude is 5, and the argument is -pi/4.

Therefore, the polar form of the complex number is:

5 * (cos(-pi/4) + i*sin(-pi/4))

Similarly, for the complex number 5√2(cos(-pi/4) + i*sin(-pi/4)), the magnitude is 5√2, and the argument is -pi/4.

Therefore, the polar form of the complex number is:

5√2 * (cos(-pi/4) + i*sin(-pi/4))To express a complex number in polar form, we use the magnitude (or modulus) and argument (or angle) of the complex number.

For the complex number 5(cos(pi/4) + i*sin(pi/4)), the magnitude is 5, and the argument is pi/4.

Therefore, the polar form of the complex number is:

5 * (cos(pi/4) + i*sin(pi/4))

Similarly, for the complex number 5√2(cos(pi/4) + i*sin(pi/4)), the magnitude is 5√2, and the argument is pi/4.

Therefore, the polar form of the complex number is:

5√2 * (cos(pi/4) + i*sin(pi/4))

For the complex number 5(cos(-pi/4) + i*sin(-pi/4)), the magnitude is 5, and the argument is -pi/4.

Therefore, the polar form of the complex number is:

5 * (cos(-pi/4) + i*sin(-pi/4))

Similarly, for the complex number 5√2(cos(-pi/4) + i*sin(-pi/4)), the magnitude is 5√2, and the argument is -pi/4.

Therefore, the polar form of the complex number is:

5√2 * (cos(-pi/4) + i*sin(-pi/4))To express a complex number in polar form, we use the magnitude (or modulus) and argument (or angle) of the complex number.

For the complex number 5(cos(pi/4) + i*sin(pi/4)), the magnitude is 5, and the argument is pi/4.

Therefore, the polar form of the complex number is:

5 * (cos(pi/4) + i*sin(pi/4))

Similarly, for the complex number 5√2(cos(pi/4) + i*sin(pi/4)), the magnitude is 5√2, and the argument is pi/4.

Therefore, the polar form of the complex number is:

5√2 * (cos(pi/4) + i*sin(pi/4))

For the complex number 5(cos(-pi/4) + i*sin(-pi/4)), the magnitude is 5, and the argument is -pi/4.

Therefore, the polar form of the complex number is:

5 * (cos(-pi/4) + i*sin(-pi/4))

Similarly, for the complex number 5√2(cos(-pi/4) + i*sin(-pi/4)), the magnitude is 5√2, and the argument is -pi/4.

Therefore, the polar form of the complex number is:

5√2 * (cos(-pi/4) + i*sin(-pi/4))