Goniometric form

Determine goniometric form of a complex number
z=30+2iz = \sqrt{ 30 } +2 i
.

Result

Mod z =  5.83
Arg z =  20.06 °

Solution:

Mod z=∣z∣=(Re z)2+(Im z)2=30+4=5.83Mod \ z = |z| = \sqrt{ (Re \ z)^2 + (Im \ z)^2 }= \sqrt{ 30 + 4 } = 5.83
tan⁡φ=Im zRe z=230=0.365 φ=atan2(2,30)  Arg z=φ=20.06∘=20∘3′34"  z=30+2i=5.83(cos⁡20∘3′34"+isin⁡20∘3′34")\tan \varphi = \dfrac{ Im \ z }{ Re \ z} = \dfrac{ 2 }{ \sqrt{ 30 } } = 0.365 \ \\ \varphi = atan2(2, \sqrt{ 30 }) \ \\ \ \\ Arg \ z = \varphi = 20.06 ^\circ = 20^\circ 3'34" \ \\ \ \\ z = \sqrt{ 30 } +2 i = 5.83( \cos 20^\circ 3'34" + i \sin 20^\circ 3'34")

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Tips to related online calculators
Try our complex numbers calculator.
Most natural application of trigonometry and trigonometric functions is a calculation of the triangles. Common and less common calculations of different types of triangles offers our triangle calculator. Word trigonometry comes from Greek and literally means triangle calculation.
Pythagorean theorem is the base for the right triangle calculator.

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