A complex mumber in rectangular form e= a+ ib = ri+ iy can also be represent in polar form or trigonometric form. Im(2) z=x+iy X Re(2) Simple connection between Polar and cartesian or rectangular coordinate form of repre- sentation of a point. Points in rectangular form are represented as (a, 6) = (r, y) and in polar coordinates as (r,0), where r = a = r cose and y = b =r sin 0. So, e = a + ib can be represent as c=r cos0+risin@ = r(cos@+i sin 0)= rais(@) The angle 0 is called the argument of e denoted by arg(c) 0 and r is called the modulus or absolute value or magnitude of c. Polar coordinates representation is very useful when we multiply or divide complex num- bers. Entering complex number in MATLAB: Type: c3 = -1+ 4i : 4 -2 -31 : 5 5 Type: c6 2i Finding magnitude and argument of a given complex mumber. Type: a3 = angle(c3) Type: a4 = angle(c4) Type: 13 = abs(c3) Type: r4 = abs(c4) Type: r5 = abs(c5) Type: r6 = abs(c6) Type: a5 = angle(c5) Type: a6 = angle(c6) Given magnitude and argument of a complex number, one can construct the rectangular form of it using the following: Type: z= r3."exp(i*a3) Type: z= r4."exp(i*a4) Exercise 1: Write the given complex number in polar form as e= r(cose+i sin e) = reis(@): a.) c10 = -1-i b.) cll =7+ 2i c.) cl2 = 3 - i. Exercise 2: Write the given complex number in rectangular coordinates (recall that the angels are in radians) : a.) e13 3cis() = 3(cos()+i sin() b.) cl4 = 6cis() c.) cl5 = 3cis(4.2)