Question

A complex number z1 has a magnitude |z1| = 2 and has an angle theta1 =49, express z1 in rectangular form, as z1= a+bi

Answer 1

To express the complex number z1 in rectangular form, we can use the formula z1 = |z1|(cos(theta1) + i*sin(theta1)). Given that |z1| = 2 and theta1 = 49 degrees, we substitute these values into the formula. Now, we can evaluate the cosine and sine of 49 degrees using a scientific calculator to get the real and imaginary parts of the complex number.

Step-by-step explanation:

To express the complex number z1 in rectangular form, we can use the formula z1 = |z1|(cos(theta1) + i*sin(theta1)).

Given that |z1| = 2 and theta1 = 49 degrees, we substitute these values into the formula.

z1 = 2(cos(49) + i*sin(49))

Now, we can evaluate the cosine and sine of 49 degrees using a scientific calculator to get the real and imaginary parts of the complex number.