Complex Number

Study Material (PDF)
Self Assesment
Study Material (PDF)
Self Assesment

Click on each question to see answer & solution.

Question No: #11

Find the condition to become purely real & purely imaginary of the expression `(a+ib)\cdot(c+i\d)`

Question No: #12

Find the modulus of following complex numbers --
i) `\frac{1}{1-i}`
ii) `\frac{-i}{1+i}`
iii) `\frac{1-i}{\sqrt{5}-i\sqrt{3}}`
iv) `(a-ib)^2`
v) `(3i-1)^2`

Question No: #13

Find argument or principal value of amplitude of following complex numbers --
i) `3i`
ii) `-3-\sqrt{3}i`
iii) `\frac{1}{1+i}`
iv) `-2`

Question No: #14

Find modulus & amplitude of following complex numbers --
i) `1+i\tan\frac{3\pi}{5}`
ii) `1 + i\tan\frac{4\pi}{7}`
Ans: i) Modulus = `- \sec \frac{3\pi}{5}` and amplitude = `- \frac{2\pi}{5}`
ii) Modulus = `- \sec \frac{4\pi}{7}` and amplitude = `- \frac{3\pi}{7}`
SEE SOLUTION

Question No: #15

Express the following complex numbers into modulus-amplitude form --
i) `\sqrt{3}-i`
ii) `\frac{i}{1-i}`
iii) `\frac{\sqrt{3}-i}{1-\sqrt{3}i}`

Question No: #16

If `iz^2 - \bar{z}=0`, then find `|z|`
Ans: 0,1
SEE SOLUTION

Question No: #17

If `8iz^3 + 12z^2 - 18z + 27i=0` then find `|z|`
Ans: `3/2`
SEE SOLUTION

Question No: #18

If `|z - 6/z| = 2` then find maximum & minimum value of `|z|`, where `|z|` is a complex number.
Ans: `1+\sqrt{7}`, `0`
SEE SOLUTION

Question No: #19

If `z` is a complex number, then find the minimum value of `|z| + |z-1|`

Question No: #20

If `z` is a complex number and `|z + 2/z| = 2`, then find maximum value of `|z|`