Simplify the following and express in the form a + ib. (1 + 3i)^2 (3 + i)

Correct option is (A) \(\frac{13}{4}\) 3.25 = \(\frac{325}{100}=\frac{13}{4}\)

Correct option is (A) \(\frac{13}{4}\) \(3.25=\frac{325}{100}\) \(=\frac{325\div25}{100\div25}=\frac{13}{4}\)

Let z = -i = 0 – i a = 0, b = -1 z lies on negative imaginary Y-axis. |z| = r = \(\sqrt{a^2+b^2}=\sqrt{0^2+(-1)^2}=1\) and  θ = amp z = 270° = \(\frac{3\pi}2\)   The polar form of z...

Let z = -1 = -1 + 0.i a = -1, b = 0 z lies on negative real X-axis. |z| = r = \(\sqrt{a^2+b^2}\) = \(\sqrt{(-1)^2+0^2}\) = 1 and θ = amp z = 180° = π The...

3 + √-64 = 3 + √64 √-1 = 3 + 8i

(2i3)2 = 4i6 = 4(i2)3 = 4(-1)3 = -4 …..[∵ i2 = -1] = -4 + 0i

(2 + 3i)(1 – 4i) = 2 – 8i + 3i – 12i2 = 2 – 5i – 12(-1) …..[∵ i2 = -1] = 14 – 5i

Correct Answer - Communication