Convert the following to polar form, answer in radians (i) 1 + j3 (ii)5 - j2 In general, the picture of a + jb is the vector that connects the origin (0,0) to the point (a,b) Therefore, the picture of 1 + j3 is the vector that connects the origin to the point (1,3) is this vector:Now we draw in the y-coordinate: That triangle has base 1, and the green side is 3, so the vector is the hypotenuse and that equals _____ ___ __ Ö1²+3² = Ö1+9 = Ö10 The angle between the vector and the x-axis has a tangent of 3/1, so the angle is 1.249 radians, approximately. So the polar form can be written any of the following ways: __ Ö10[sin(1.249) + j·cos(1.249)] __ Ö10 cjs(1.249) __ Ö10 Ð 1.249 ------ (ii)5 - j2 The picture of 5 - j2 is the vector that connects the origin to the point (5,-2) is this vector: Now we draw in the y-coordinate: That triangle has top side 5, and the green side is -2, so the vector is the hypotenuse and that equals ________ ____ __ Ö5²+(-2)² = Ö25+4 = Ö29 The angle between the vector and the x-axis has a tangent of -2/5, so the angle is -.381 radians, approximately. So the polar form can be written any of the following ways: __ Ö29[sin(-.381) + j·cos(-.381)] __ Ö29 cjs(-.381) __ Ö29 Ð -.381 Edwin