Question

Convert the following complex number into its polar representation -4i

Answer 1

The expression which represent the polar form of complex number -4i when converted into the polar form is 4(cos π+ isin π)

What is complex number?

A complex number is the combination of real and imaginary number. In a complex number, real part and imaginary part of number is written together. For example,

a+bi

Here, (a) is the real part while (b) is the imaginary part.

The complex number which need to convert into its polar representation is,

n=-4i

It can be rewritten as,

n=0-4i

The radius r of the polar form is,

r²=0²+(-4)²

r²=0+16

r=4

The value of cos theta is,

tan θ=0/-4

θ=tan⁻¹(0)

θ=π

Thus, the polar form is,

z=rcos θ+(r sin θ)i

z=-4(cos π+ isin π)

Thus, the expression which represent the polar form of complex number -4i when converted into the polar form is 4(cos π+ isin π)

Learn more about the complex number here;

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