- What is complex numbers
- |
- Properties Of complex Numbers
- |
- Conjugate of Complex Numbers
- |
- Modulus of complex numbers
- |
- Graphical Representation of Complex Number
- |
- Polar Representation of the complex number
- |
- Rotation of Complex Number
- |
- What is the significance of Complex Numbers

**Question 1:**

Express the given complex number in the form a + ib: (5i)(-3i/5)

**Question 2:**

Express the given complex number in the form a + ib:

i^{9} +i^{19}

**Question 3:**

Express the given complex number in the form a + ib: i^{-39}

**Question 4:**

Express the given complex number in the form a + ib: 3(7 + i7) + i(7 + i7)

**Question 5:**

Express the given complex number in the form a + ib: (1 – i) – (–1 + i6)

**Question 6:**

Express the given complex number in the form a + ib:

(1/5+2i/5)-(4+i5/2)

**Question 7:**

Express the given complex number in the form a + ib:

**Question 8**

Express the given complex number in the form a + ib: (1 – i)^{4}

**Question 9:**

Express the given complex number in the form a + ib: (1/3+3i)^{3}

**Question 10**

Express the given complex number in the form a + ib: (-2-1i/3)^{3}

**Question 11:**

Find the multiplicative inverse of the complex number 4 – 3i.

**Question 12:**

Find the multiplicative inverse of the complex number

**Question 13**

Find the multiplicative inverse of the complex number –i

**Question 14**

Express the following expression in the form of a + ib.

**Solution 1**

(5i)(-3i/5)

Multiplying

=-(15/5)i^{2}

Now we know that

i^{2}=-1

so

=3

**Solution 2**

i^{9} +i^{19}

=i^{2X4 +1} +i^{4X4 +3}

=(i^{2})^{4} I + (i^{4})^{4} i^{3}

Now i^{2}=-1 so i^{4}=1 and i^{3}=-i

=i+(-i)

=i-i=0

**Solution 3**

**Solution 4:**

3(7 + i7) + i(7 + i7)

=21+21i+7i+7i^{2}

Now i^{2}=-1

So

=21+28i-7

=14+28i

**Solution 5:**

(1 – i) – (–1 + i6)

**=2-7i **

**Solution 6:**

(1/5+2i/5)-(4+i5/2)

=[(1/5)-4] +i[(2/5) –(5/2)]

=(-19/5) +(-21/10)i

**Solution 7:**

**Solution 8**

(1 – i)^{4}

**Can be written as**

**=**[(1-i)^{2}]^{2}

=(1+i^{2}-2i)^{2}

=(1-1-2i)^{2}

=4i^{2}=-4

**Solution 9**

**Solution 10**

**Solution 11**

Let z=4-3i

Conjugate is given by

=4+3i

Modulus is given by

|z|=5

Multiple inverse of any complex number z is given by

**Solution 12**

Let z= √5+3i

Conjugate is given by

= √5-3i

Modulus is given by

|z|=5+9=14

Multiple inverse of any complex number z is given by

**Solution 13**

Let z=-i

Conjugate is given by

=i

Modulus is given by

|z|=1

Multiple inverse of any complex number z is given by

**Solution 14**

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