# Find ##z## in the form ##a+bi## under Complex Numbers

• chwala
In summary, complex numbers are numbers that contain both a real part and an imaginary part. To add or subtract complex numbers, the real and imaginary parts are combined separately. The complex conjugate is formed by changing the sign of the imaginary part and is useful for dividing complex numbers. To multiply complex numbers, the FOIL method is used, and to divide, the conjugate of the denominator is multiplied. To find the value of z in the form a+bi, the real and imaginary parts are identified and solved for.
chwala
Gold Member
Homework Statement
see attached
Relevant Equations
Complex numbers

For part (a),
##z##=##\dfrac {3+i}{3-i}## ⋅##\dfrac {3+i}{3+i}##
##z##=##\dfrac {4}{5}##+##\dfrac {3}{5}i##

part (b) no problem as long as one understands the argand plane...

For part (c)
Modulus of ##z=1##
and Modulus of ##z-z^*##=##\frac{6}{5}i##

Last edited:
The modulus is a real number, so it can't be ##\frac 6 5 i##.

PeroK said:
The modulus is a real number, so it can't be ##\frac 6 5 i##.
True, its supposed to be ##\dfrac {6}{5}##

## 1. How do I find the real and imaginary parts of a complex number?

To find the real and imaginary parts of a complex number in the form a+bi, simply separate the real and imaginary numbers. The real part is represented by a, and the imaginary part is represented by bi.

## 2. What is the difference between a real number and a complex number?

A real number is a number that can be represented on a number line, such as 3 or -2. A complex number is a number that contains both a real and imaginary part, and is represented in the form a+bi.

## 3. How do I add or subtract complex numbers?

To add or subtract complex numbers, simply combine the real parts and the imaginary parts separately. For example, (3+2i) + (1-4i) = (3+1) + (2i-4i) = 4 - 2i.

## 4. Can I multiply or divide complex numbers?

Yes, you can multiply and divide complex numbers by following the same rules as for real numbers. To multiply, use the distributive property and combine like terms. To divide, multiply the numerator and denominator by the complex conjugate of the denominator.

## 5. How do I find the modulus or absolute value of a complex number?

The modulus or absolute value of a complex number is the distance from the origin (0,0) to the point representing the complex number on the complex plane. It can be found using the Pythagorean theorem as |z| = √(a² + b²).

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