Consider (cosine (startfraction pi over 2 endfraction) = i sine (startfraction pi over 2 endfraction) ) and z = 3 (cosine (start

Question

2 years ago

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fraction 3 pi over 2 endfraction) = i sine (startfraction 3 pi over 2 endfraction) ).. what is w z expressed in polar form?

1 answer:

Gemiola [76] · Answer 1 · 2023-05-14T15:45:23+03:00

Sum of given complex numbers in polar form cos(pi/2) + i.sin(pi/2)

Complex number:

"The number of the type a + ib is called as complex number, where a, b are real numbers and $i= \sqrt{-1}$

What is polar form of the complex number?

"The polar form of a complex number z = x + iy

For given question,

The sum of given complex numbers would be w+z = 4cos(pi/2 + i sin(pi/2)+ 3 cos (3pi/2) + i sin(pi/2)

We know that:

cos(pi/2)= 0

sin(pi/2)=1

cos(3pi/2)=0

So, the sum of given complex numbers would be w+z:

=> 4cos(pi/2 + i sin(pi/2)+ 3 cos (3pi/2) + i sin(pi/2)

=> 4i + 3(-i)

= i

= 0+i

Therefore, the sum of given complex numbers in polar form as:

cos(pi/2) + i.sin(pi/2)

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