Question

write polar, carnation,argument, angele , ,and rectangular form of thi Complex number (1+3i)(3+4i)(-5+3i)

Answer 1

Rectangular form:

z = 6-92i

 

Angle notation (phasor):

z = 92.1954446 ∠ -86°16'7″

 

Polar form:

z = 92.1954446 × (cos (-86°16'7″) + i sin (-86°16'7″))

 

Exponential form:

z = 92.1954446 × ei -1.5056712 = 92.1954446 × ei (-0.47927) π

 

Polar coordinates:

r = |z| = 92.1954446 ... magnitude (modulus, absolute value)

θ = arg z = -1.5056712 rad = -86.2686° = -86°16'7″ = -0.47927π rad ... angle (argument or phase)

 

Cartesian coordinates:

Cartesian form of imaginary number: z = 6-92i

Real part: x = Re z = 6

Imaginary part: y = Im z = -92

(1+3i) * (3+4i) = 1 * 3 + 1 * 4i + 3i * 3 + 3i * 4i = 3+4i+9i+12i2 = 3+4i+9i-12 = 3 - 12 +i(4 + 9) = -9+13i

and (-9+13i) * (-5+3i)

= -9 * (-5) + (-9) * 3i + 13i * (-5) + 13i * 3i = 45-27i-65i+39i2

= 45-27i-65i-39

= 45 - 39 +i(-27 - 65) = 6-92i