The complex number z = 4 into its rectangular form
What is complex number?
Every complex number may be represented in the form a + bi, where a and b are real numbers. A complex number is an element of a number system that extends the real numbers with a specific element labeled I sometimes known as the imaginary unit, and satisfying the equation i² = 1.
Given
* Lets revise the complex numbers
- If z = r(cos Ф ± i sin Ф), where r cos Ф is the real part and i r sin Ф is the imaginary part in the polar form
- The value of i = √(-1) ⇒ imaginary number
- Then z = a + bi , where a is the real part and bi is the imaginary part
in the rectangular form
∴ a = r cos Ф and b = r sin Ф
* Lets solve the problem
∵ z = r (cos Ф ± i sin Ф)
∵ z = 4 (cos π/2 + i sin π/2)
∴ The real part is 4 cos π/2
∴ The imaginary part is 4 sin π/2
- Lets find the values of cos π/2 and sin π/2
∵ The angle of measure π is on the positive part of x axis at the
point (0 , 4)
∵ x = cos π/2 and y = sin π/2
∴ cos π/2 = 0
∴ sin π/2 = 1
∴ a = 4(0) = 0
∴ b = 4(1) = 4
∴ z = 0 + i (4)
* The complex number z = (0,4) into its rectangular form
To learn more about complex numbers refer to:
https://brainly.com/question/12842137
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