Question

Using Euler's formula, represent the following complex numbers in the Polar form (i.e., rᵉrho).

(a) 1+j2;
(b) 1−j2.

Answer 1

To represent complex numbers in polar form, use Euler's formula, which states that for any complex number z = a + bi, the polar form is z = r*e^(i*theta), where r is the magnitude and theta is the argument in radians.

Step-by-step explanation:

To represent complex numbers in polar form, we can use Euler's formula, which states that for any complex number z = a + bi, where a and b are real numbers, the polar form is given by z = r*e^(i*theta), where r is the magnitude of the complex number and theta is the argument in radians.

(a) For the complex number 1 + j2, we can calculate its magnitude as r = sqrt(1^2 + 2^2) = sqrt(5). To find the argument, we can use the arctan function: theta = arctan(2/1) = arctan(2) ≈ 1.11 radians. Therefore, the polar form is approximately sqrt(5) * e^(i*1.11).

(b) For the complex number 1 - j2, the magnitude remains the same as in part (a), but the argument becomes -1.11 radians. Hence, the polar form is approximately sqrt(5) * e^(-i*1.11).