Cis notation

Evaluate multiplication of two complex numbers in cis notation:

(6 cis 120°)(4 cis 30°)

Write result in cis and Re-Im notation.

Result

c = (Correct answer is: 12 cis 150°)
R =  -10.3923
I =  6

Step-by-step explanation:

$$\begin{gathered} A=3\cdot 4=12 \\ \alpha =120+30=150\text{ ° } \\ c=12cis150\mathrm{°} \end{gathered}$$

$R=A\cdot \cos \alpha \mathrm{°}=A\cdot \cos 150\mathrm{°}=12\cdot \cos 150\mathrm{°}=12\cdot (-0.866025)=-10.392=-10.3923$

$I=A\cdot \sin \alpha \mathrm{°}=A\cdot \sin 150\mathrm{°}=12\cdot \sin 150\mathrm{°}=12\cdot 0.5=6=6$

Try another example

Related math problems and questions:

• Inner angles
  The inner angles of the triangle are 30°, 45° and 105° and its longest side is 10 cm. Calculate the length of the shortest side, write the result in cm up to two decimal places.
• Scalar dot product
  Calculate u.v if |u| = 5, |v| = 2 and when angle between the vectors u, v is: a) 60° b) 45° c) 120°
• Bearing
  A plane flew 50 km on a bearing 63°20' and the flew on a bearing 153°20' for 140km. Find the distance between the starting point and the ending point.
• Two forces
  Two forces with magnitudes of 25 and 30 pounds act on an object at 10° and 100° angles. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and your final answer.
• Tetrahedral pyramid
  Determine the surface of a regular tetrahedral pyramid when its volume is V = 120 and the angle of the sidewall with the base plane is α = 42° 30'.
• Bearing - navigation
  A ship travels 84 km on a bearing of 17° and then travels on a bearing of 107° for 135 km. Find the distance of the end of the trip from the starting point, to the nearest kilometer.
• Observer
  The observer sees a straight fence 100 m long in 30° view angle. From one end of the fence is 102 m. How far is it from another end of the fence?
• Internal angles
  The ABCD is an isosceles trapezoid, which holds: |AB| = 2 |BC| = 2 |CD| = 2 |DA|: On its side BC is a K point such that |BK| = 2 |KC|, on its side CD is the point L such that |CL| = 2 |LD|, and on its side DA the point M is such that | DM | = 2 |MA|. Dete
• Evaluate 18
  Evaluate the expression (-4-7i)-(-6-9i) and write the result in the form a+bi (Real + i* Imaginary).
• Resultant force
  Calculate mathematically and graphically the resultant of three forces with a common center if: F1 = 50 kN α1 = 30° F2 = 40 kN α2 = 45° F3 = 40 kN α3 = 25°
• Airplane navigation
  An airplane leaves an airport and flies to west 120 miles and then 150 miles in the direction S 44.1°W. How far is the plane from the airport (round to the nearest mile)?
• Hot air balloon
  The center of the balloon is at an altitude of 600 m above the ground (AGL). From habitat on earth is the center of the balloon to see in elevation angle 38°20' and the balloon is seen from the perspective of angle 1°16'. Calculate the diameter of the bal
• Triangles
  Find out whether given sizes of the angles can be interior angles of a triangle: a) 23°10',84°30',72°20' b) 90°,41°33',48°37' c) 14°51',90°,75°49' d) 58°58',59°59',60°3'
• Right triangle trigonometrics
  Calculate the size of the remaining sides and angles of a right triangle ABC if it is given: b = 10 cm; c = 20 cm; angle alpha = 60° and the angle beta = 30° (use the Pythagorean theorem and functions sine, cosine, tangent, cotangent)
• Building
  The building I focused at an angle 30°. When I moved 5 m building I focused at an angle 45°. What is the height of the building?
• Viewing angle
  The observer sees a straight fence 60 m long at a viewing angle of 30°. It is 102 m away from one end of the enclosure. How far is the observer from the other end of the enclosure?
• Moivre 2
  Find the cube roots of 125(cos 288° + i sin 288°).