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Chapter 1: Q10P (page 1)

First simplify each of the following numbers to the x+iy form or to the rei胃 form. Then plot the number in the complex plane.

3i-7i+4 .

Short Answer

Expert verified

The complex number becomes 5817e142.8i.

Step by step solution

01

Given Information

The complex number is3i-7i+4 .

02

Definition of the Complex number

A complex number is a number that is made up of both real and imaginary numbers.

03

Find the value

The complex number is 3i-7i+4 .

Rationalize the complex number.

z=-7+3i4+i脳4-i4-i=-28+19i-3i216-i2=-25+19i17z=-2517+19i17

Find x and y.

z=x+iyz=-2517+19i17x=-2517y=1917

Find the value of r.

localid="1664175531640" r=x2+y2r=625289+361289=986289=5817

Find the value of 胃.

胃=cos-1xr胃=cos-1--25175817胃=142.80

The complex number becomes 5817e142.8i.

The graph is mentioned below.

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