Goniometric form

Determine the goniometric form of a complex number

$z=\sqrt{110}+4i$

.

Correct answer:

Mod z =  11.22
Arg z =  20.88 °

Step-by-step explanation:

$Modz=\mathrm{\mid }z\mathrm{\mid }=\sqrt{(Rez{)}^2+(Imz{)}^2}=\sqrt{110+16}=11.22$

$$\begin{gathered} \tan \phi ={\displaystyle \frac{Imz}{Rez}}={\displaystyle \frac{4}{\sqrt{110}}}=0.381 \\ \phi =atan2(4,\sqrt{110}) \\ Argz=\phi =20.88\text{°}=20\mathrm{°}52^{\mathrm{\prime }}34\mathrm{"} \\ z=\sqrt{110}+4i=11.22(\cos 20\mathrm{°}52^{\mathrm{\prime }}34\mathrm{"}+i\sin 20\mathrm{°}52^{\mathrm{\prime }}34\mathrm{"}) \end{gathered}$$

Try another example

Related math problems and questions:

• Modulus and argument
  Find the mod z and argument z if z=i
• Moivre 2
  Find the cube roots of 125(cos 288° + i sin 288°).
• ABS CN
  Calculate the absolute value of complex number -15-29i.
• 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)?
• Space vectors 3D
  The vectors u = (1; 3; -4), v = (0; 1; 1) are given. Find the size of these vectors, calculate the angle of the vectors, the distance between the vectors.
• Triangle SAS
  Calculate the triangle area and perimeter, if the two sides are 51 cm and 110 cm long and angle them clamped is 130 °.
• Distance two imaginary numbs
  Find the distance between two complex number: z₁=(-8+i) and z₂=(-1+i).
• Angle between lines
  Calculate the angle between these two lines: p: -8x +4y +5 =0 q: 10x +10y -7=0
• V-belt
  Calculate the length of the belt on pulleys with diameters of 105 mm and 393 mm at shaft distance 697 mm.
• 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.
• 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.
• Cotangent
  If the angle α is acute, and cotan α = 1/3. Determine the value of sin α, cos α, tg α.
• Right
  Determine angles of the right triangle with the hypotenuse c and legs a, b, if: 3a +4b = 4.9c
• 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.
• The modulus
  Find the modulus of the complex number 2 + 5i
• Coordinates of square vertices
  I have coordinates of square vertices A / -3; 1/and B/1; 4 /. Find coordinates of vertices C and D, C 'and D'. Thanks Peter.
• Angle of two lines
  There is a regular quadrangular pyramid ABCDV; | AB | = 4 cm; height v = 6 cm. Determine the angles of lines AD and BV.