**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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